OK, this is the original question:
"125,000 tonnes, with a maximum tonnage of 33,000 tonnes each, would have allowed 4 ships of about 31,000 tonnes. Careful design, and construction similar to that used in the Deutschlands could have produced some impressive ships - any ideas on specifications?
What would have been the effect of these ships when WW2 broke out? They would probably remove the need for the Scharnhorst and Gneisenau, and maybe even the Bismarck and Tirpitz - or maybe the Kriegsmarine would see them as the foundation of a balanced fleet and concentrate more on the surface navy?"
Assuming for the sake of argument that the Wikipedia article is even correct that these negotiations occured, this would not have "removed the need" for the Scharnhorst class, it would have created something like them earlier. Perhaps the Germans might have gone with guns instead of armor or speed (six to eight 15' guns on something like a slow Renown), but given German predilection for staying power, together with the realization that any fleet limited to this ratio vs the other main navies would never be a real "battle fleet", they'd probably end up with something not dissimilar to OTL's Scharnhorst. Any British and French "responses" to these ships would be scaled up accordingly beyond what they built or reconstructed to counter the pocket battleships. France would go directly to something a lot more like Richelieu, and the British might expedite the modernization of Hood, Queen Elizabeths, and the Renowns, any of which were already the equal of what the Germans would be building in terms of speed and offensive power.
This might have an effect on "Treaty" heavy cruisers more than capital ships. Leaving the Japanese out of the equation for a minute - who had their own reason for building the biggest crusiers they could get away with - the fear of the pocket battleships made most other navies try to squeeze so much into 10,000 ton ships that it resulted in over armed heavy cruisers that were unbalanced. Perhaps in this scenarish fewer "heavy cruisers" would be built, with the tonnage going to more smaller and faster scout cruisers.
why on earth should the germans build such ships?
the german navy before hitler knew exactly what kind of ship they need...
fast? yes - fast enough to run away from superior ships
long ranged? yes - so diesel is important
armor? no - any ship with enough armor to protect itself against large calibres is to heavy and expensive...
weapons? yes - but politically no. a german ship with a big calibre gun will have to disadvantages for them
a.) political stress
b.) costs.. in money and space/shipsize
they knew exactly that an enlargen pocketbattleship is perfect
they even thought about diesels on the scharnhorsts...
in this scenario they COULD build ships with only two turrets (2x3) and 28cm guns (for money, time and political things) but long range and better armour. They would build the pbs with more armor, but couldn´t... they had been out of the legal size, with more armor they had been fully out of the scale
so if they make this deal, a ship with 2x3 28cm guns and long range and high speed but cruiserproven armor is the logical ship
maybe they do not need 25/29000ts... maybe they can build it with 20.000ts (full deplacement around 26000ts, the 25/29000ts would be full displaced aroound 34/35000ts)
sure, some would like to build later (if they are liberated from versailles) to build "better" and stronger ships, with more punch, but they will run out of time and money... could some plans exist (or ships even been layed down?) yes... maybe something like bismarck, with more protection (cause the allied reactions (known in the late 30ties) will let the germans build the H-class with more armor and range even earlier...
honestly, the germans tried to reach range with the conventional engines, but they ignored completly that such engines could not be worked at economical level (with this the scharnhorst had an enormous range - but in reality it was only 30% of this, same is true for heavy cruisers and destroyers... )