In the late 30s Britain had a total of 9 large gun pits capable of reconditioning the twin 15" Mk1n Turrets found on the refits and/or making new turrets for the KGVs / Lions and from what I recall reconditioning a turret or building a new one took about 8-12 months - if you start stacking up turrets to recondition then you are not building new ones - the Italians had the same issue in their rebuilds seriously delayed the modern units.
I'd say stick with the Quad 14" and have all 3 turrets as Quads and build 6 units (the 6th being Vanguard as a KGV) as quickly as possible from Jan 1st 1936 and don't bugger about with the turrets or Guns stick with 3x4x14" and be done with it. The delay in designing and building the twin 14" turrets delayed the ship's - deal with the stability issues and get them built ASAP. If time allows the follow on 6 Lions can have more time spared on them
My plan was not to build any new guns or mounts (ever again but might not advertise that fact) so just rebuilding 15" mounts to Mark I/N standard, as this has already been started for Warspites rebuild its should be easier to complete fast as its a known design. The 14" systems are all cancelled (and later 16" never leave the paper stage).
9 pits working on an 8 month cycle gives you 13 mounts a year so that would easily do the 16 for the Vanguards. The question is can I also do the 12 more needed for the three OTL rebuilds (QE/V/R) that happened after Warspite's I'm not sure but rebuilding 16 must be less than building all the new larger mounts 10xQuads 5xTwins (+ wasted effort on Lion triples). I may have to open the old smaller pits earlier to fit them?
I just don't see much if any advantage to 14" over 15" (or even 16") they will all do the job v German or Italian ships and I would rather have 15" with far fewer issues sooner.
The quad turret appears to have been a bug-a-boo that the Brits didn't solve fast enough, why not just replace the 10-14" with 9 in the form of 3 triples and be done with it?
I think any new turret would have been a problem, due to the short time frame available. The RN looks like it did not have sufficient competent mount designers post WWI if you look at the 16"/14"/4.5"/5.25"/etc they all suffered.
As for the 5.25" guns their range and max altitude make a lot sense when you consider than in 1936 Bombers are flying higher and faster carrying more bombs and Destroyers/Crusiers are getting bigger and firing torpedos from further away - radar directed twin 5" guns firing Proximity fused ammo is science fiction at this time.
The 4.5" with new split ammo will work fine, the 5.25" was more balanced for surface fire than AA and with hindsight that's far less important, its also a later design so I would far rather cut it to save on the number of new calibres, ie all new ships would be 4.5" (cancel new 4.7"/45, 4.7"/50 and 5.25").
As is the practical application of Radar so the shagbats stay as well
No they go on the rebuild Hawkins/CLs as fast AA escorts to minimize fire risks and free space for more AA...
Draw a line under the design as early as possible, order them all in 1936 and get building them ASAP laid down as close as possible to Jan 1st 1937 - have all launched by end of year 1939 (plan to lay down the Lions as soon as the slipway is free!) and all 6 in commission in 1940/41 and the Lions plan to be launched during 42 and all in commission by 1944 - War notwithstanding!
- perfection is the enemy of the good enough as they say! (it might have been Arther C Clark wot said it)
I don't think you need that much, 4 Vanguards in 39 is worth far more than any number of KVGs in 42 or Lions in 44. The need is for fast ships to match the German raider PBs/CAs/S&G/B&T as well as potentially the RMs 12.6" and 15" ships for the vital 39-42 time frame having 7 fast ships 4V +H and R&R is far better than OTL(I would love your 6 KVGs but cant see how that doesn't eat massively more production than my 4 Vanguards ?)