AHC/WI: Faster Nelson class?

Are there enough second hand 7.5in guns to be of any real use on new cruisers?
7.5"/45 Mk I production reached all of 33 guns including prototypes, four lost with HMS Hampshire.
the Mark III and IVs reach all of 32 guns produced, of which 14 were lost aboard HMS Triumph off Gallipoli, one aboard M21 in the Channel, one aboard M25 scuttled in the Dvina river.
the 7.5"/50 Mk II and Mk V had production runs of 21 (plus 14 coast defence guns) and 40 respectively, of which four lost aboard HMS Warrior at Jutland, another four likely lost when HMS Natal blew up in port, 10 lost with HMS Defence at Jutland

That gives us a total of 29 Mk Is + 16 Mk III/IVs + 43 Mk II/Vs without factoring in any guns being too worn out for further service; repurposed for coast defence; used as test articles and similar. Assuming nine guns per new build cruiser (say 8 mounted plus 1 in the spares pool per ship), the Mark Is could potentially equip three cruisers; the Mark III/IVs a single ship and the Mark II/Vs four cruisers.

So, utter best case you can provide for less than half of the OTL County class program. In a only marginally insane case (discard the Mk Is and Mk II/Vs), you can only fit out four ships... And you're probably gonna need to design new mountings as the single mounts off the armoured cruisers were limited to 15 degrees of elevation, constraining range to about 14000m vs the about 28000m of the 8" guns mounted on OTL County class. Using an Italian 7.5" gun of similar vintage as a proxy improved elevation might enable you to extend the 7.5" range out to about 22000m.

There might be some argument for continued 7.5"/45 Mark VI production instead of switching to an 8" gun, but you'll still probably want a new turret design, meaning you're copping a lot of the cost of moving to 8" anyway.
One of the conclusions that the RN made from WW1 and examination of German guns was that lighter shells and higher velocity increased the 'danger zone' for the target making hits more likely. As this was the opposite of pre-War RN thinking then all new guns in the 1920's is a given.

A great slab on the post war direction of RN cruisers and the influences (Source Friedman, Norman. British Cruisers: Two World Wars and After). Note that 9.2" doesn't seem to have been considered.

In January 1920 in Washington, the American Admiral Mayo explained to Dreyer that in his opinion nothing smaller could carry enough fuel to be of much use in the Pacific. The General Board, responsible for formulating US Navy programmes, recommended that year that thirty such cruisers, armed with 8in guns, be built over the next three years. The US government was unenthusiastic, and even a scaled-down plan for five cruisers in 1921 failed, but clearly future US light cruisers would be 10,000-tonners. The US Navy was reportedly planning to mount ten 8in guns in the planned ships (which seemed to be too much on that displacement). The Japanese had already announced plans for four cruisers of over 7,000 tons (the Furutakas). No details were known.

Dreyer suggested that former German officers and the French gave some pointers towards the future. To the Germans, their wartime Köln class (about 5,500 tons, eight 5.9in guns, 28.5kts) was too slow and too large for the fleet and too small for foreign service. They violated the cardinal rule that ships of inferior fighting power should be fast enough to escape superior ships. The first requirement for a ‘foreign service’ cruiser stated in 1917 was the ability to keep the sea. Speed should be 25kts for long periods and 26-29kts for short ones, to run down and examine fast merchant ships and to avoid the enemy. Guns should be 6.7in or 7.5in; the proposed armament was eight such guns in twin turrets. Torpedoes were desirable. The ship should be armoured against 6in fire. The original proposal was for 12,000 tons, but the Kaiser considered that too small and recommended 14,000 tons.

According to the Naval Attaché in Paris, Admiral Grasset argued that since the Versailles Treaty limited the Germans (still the main enemy) to 10,000 tons, France should go one better with 10,000 tons and 7in or 8in guns. No such ships had yet been ordered. Dreyer considered the French reasoning vicious, because it would start an upward spiral of cruiser development which would prevent the Royal Navy from building enough such ships (he regretted the Hawkins class, which had started the process). Overall, it was clear that cruisers were tending towards 10,000 tons.

Ideally the Royal Navy would build somewhat smaller ships in larger numbers. The places to cut would be torpedo tubes (not needed in a trade-protection cruiser) and side protection against 6in guns (it would suffice to provide a protective deck of moderate thickness).32 In any case, enough armour to defeat 7.5in or 8in guns would add prohibitive weight. Presumably torpedo tubes could be fitted if the cruiser was needed for fleet work.

As a gunner, Dreyer advocated the 8in gun because engagements would probably be fought at extreme range, and because effective range depended on the ability to observe the fall of shot. Although a 6in gun could range out to 20,000yds, only the splashes of the larger 7.5in and 8in shells could be spotted reliably at such ranges.33 Recent trials suggested, moreover, that a well-designed enemy light cruiser could not be stopped by 6in fire. Dreyer preferred the 8in gun to the 7.5in because it offered superior penetration and bursting effect for a small increase in weight. He hoped that a power-operated 8in mounting could fire five rounds per gun per minute. Ships would have no secondary LA armament, but should have four 4in HA guns for anti-aircraft and star shell. They would also need automatic weapons to counter torpedo planes and distance-controlled boats, both of which Dreyer claimed the US Navy was developing.34 Two of the multiple pompoms then being proposed by the Naval Anti-Aircraft Committee seemed adequate. Any such ship should carry one or more amphibious aircraft (Dreyer recalled the wartime German raider Wolf, which had one such aircraft). Dreyer envisaged a revolving flying-off platform for an amphibious aircraft and a crane to hoist it in. The aircraft would be used for both reconnaissance and spotting. Since the cruisers would operate mainly in the tropics, they should have improved ventilation arrangements and a magazine cooling plant.

On this basis Dreyer suggested five alternatives:
A: 10,000 tons, 31kts, eight 8in twin splinter-proof on centreline.
B: 8,500 tons, 32kts, five 8in single splinter proof on centreline.
C: 7,500 tons, 35kts, four 8in single splinter-proof on centreline.
D: 7,500 tons, 32kts, four 8in single splinter-proof on centreline.
E: 7,500 tons, 25kts, four 8in single splinter-proof on centreline.

Design A would counter the projected US 10,000-ton cruisers, if British finances permitted (the 7,050-ton Omahas would, however, outrun them). It would not be desirable to go below 7,500 tons, ‘as this is the smallest size now advocated by other countries’. Director of Plans protested that existing Japanese cruisers were much smaller, but for Dreyer the problem was what was coming, not what already existed. No 6in cruiser could effectively fight an 8in cruiser. Dreyer preferred a 7,500-tonner armed with four centreline 8in guns (he was willing to accept 7.5in if DNC could not provide power hoists and power ramming while providing the desired endurance, maximum speed, and other items on the tonnage [i.e. on a limited cost]). The armament decision seemed urgent, if a concrete plan was to be presented to the Imperial Conference. Dreyer particularly cautioned that the Dominion governments should not be misled into imagining that they were being asked for nothing more than the wartime fleet cruisers. However, he also feared that buying cruisers comparable to the largest ones being planned abroad might (as with the Hawkins class) lead other navies to build even larger ships. Hence his preference for the four-gun 7,500-tonner. He also warned that, given his own experience over the last seven years, it might be some years before any Dominion ordered a new light cruiser. He did not make the implication explicit: some or all of those trade protection ships would have to come out of Royal Navy funds. Of the alternatives listed, C to E differed in endurance and protection. Cruiser E was a minimum ship for convoy protection, but she would be unable to attack or run down enemy cruisers. In effect Dreyer had described the next step in cruiser development.
DCNS agreed that any new trade protection light cruisers would have to be armed with (at least) 7.5in guns, and would probably be comparable to the big Hawkins type. He doubted that a ship of smaller displacement could combine sufficient radius of action and armament.

The problem was numbers. In July 1918, when practically all trade between North America and Europe was being convoyed, as well as a proportion of vessels outward bound to North America, and ships operating between Great Britain and Sierra Leone and Dakar, convoys required no fewer than seventy ocean escorts, including cruisers, armed merchant cruisers and commissioned escort ships. A worldwide convoy system would have required about 150 ocean escorts (apart from ASW ships in local escort groups). The most powerful potential Japanese raiders were the four Kongo class battlecruisers, which could be contained only by their British equivalents. For this reason the Royal Navy periodically considered stationing some or all of its battlecruisers in the Far East (a plan to this effect was nearly put into effect in 1929). However, a smaller number of unusually powerful British cruisers working with convoys could make Japanese attacks on convoys too risky. To attack Empire commerce, any Japanese cruisers would have to operate far from their bases; even limited damage might prove fatal (as was the case with the German Admiral Graf Spee in 1939). The wartime ‘large light cruisers’ (Courageous class) might be a useful model for future construction. In the past cruiser size had been held down to make it possible to build such ships in quantity, particularly for fleet operations. However, the fleet might need fewer cruisers if the promise of carrier-borne reconnaissance aircraft was realised. Five Courageous-class cruisers would cost about as much as eight Hawkins.

ACNS suggested (and DCNS agreed) to ask DNC to consider two alternatives. One would be a 33kt 10,000-tonner armed with 7.5in or 8in guns, without torpedo tubes, and otherwise as Dreyer had proposed. Endurance would be 5,500nm at 16kts, and in contrast to the wartime Hawkins, the ship would burn only oil fuel. The second would have much the same characteristics, but with more powerful (preferably 10in) guns, and magazines protected against 8in fire. Maximum displacement would be 15,000 tons. DCNS added that the term Commerce Protection Cruiser should be dropped in favour of some alternative, preferably Station Cruiser – which would recall the much earlier practice of keeping powerful armoured cruisers on the foreign stations, for presence as well as for trade protection. The Dominions should want a ship which could go anywhere and fight anything short of a battlecruiser.

DNC could not produce the desired pair of designs, because his department was fully occupied producing the new battleship and battle-cruiser designs as well as other vital work (including the cruiser-sized minelayer described in the Appendix and the flush-deck carrier conversion of HMS Furious), but he produced some quick estimates.35 His main conclusion was that the Staff had grossly underestimated what was needed to achieve either the desired speed or the desired endurance. For example, using lightweight (‘E’ class) machinery, an enlarged Hawkins (11,000 tons) might make 31kts. To achieve the desired endurance, the ship would have to be lengthened to about 600ft (about 12,000 tons). To make 33kts, she would need about 30 per cent more power (using lightweight machinery, about 12,500 tons). To provide deck space for the amphibian, she would have to concentrate her armament (six rather than seven 7.5in) in three twin turrets; without the amphibian she could probably have another pair of such guns. The proposed 10in ship would probably be about the size of HMS Courageous (19,000 tons).
Because with the 9.2-inch you need a bigger and more expensive ship, you'd need new turret designs and to fit a decent number of guns (IE 8) with the speed, range and other requirements the RN wanted for its large cruisers, you're probably looking at a 14 - 16k ton ship that'll be longer and beamier than the Counties.
Basically weight. Inter war the RN moved to full built up guns with significant weight savings. Even the 16" on the Nelsons were a halfway step.
My question is were the RN able to re-sleeve the guns, which was a possibility I believe with barrels after heavy use, especially with limited numbers produced?
My question is were the RN able to re-sleeve the guns, which was a possibility I believe with barrels after heavy use, especially with limited numbers produced?
The British made 29 guns and definately did reline the barrels. It is discussed on the Navweaps site in reference to two kinds of rifling and as the war went on the turrets got guns with different rifling.