The Twins being built with 6x15" might well butterfly the KGV class - resulting in Lions instead.
Unless the Germans are going to accept major delays in completion not possible to build with 15" guns. The entire design history of Cruiser D, Twins and Bismarck's was a twisted mess where they bounced around on displacement and armaments. Both D and Scharnhorst were laid down without plans being complete. The 12 15" guns just can't be ready in the time period. On the British side they felt obligated to follow first London and they had already used up their two ships larger than 14" guns on the Nelsons. RN couldn't build more till escalator clause of Second London kicks in and by then it was too late for King George V class. The 15" gun designs were just design studies and we're going to be built.
I was going to name one of the 3 extra ships Admiral Souchon until I discovered that he didn't die until 1946. As an aside, Scheer and Hipper both had von in their name so why weren't the ships named after them the Admiral Graff Hipper and Admiral Graff Scheer?
Graf is German for Count. Spee was a titled noble while the rest were just members of nobles families. Being alive wouldn't be an issue see WW1 ships Hindenburg and Mackensen.
The Treaty of Versailles set the replacement age of a battleship at 20 years and all 8 of the pre-dreadnoughts retained after 1919 were "over 20" by 1928. There should be enough vacant slipways of the required size between 1928 and 1933 because of the Depression and I thought the Weimar Government could justify the cost as an unemployment relief measure.
I doubt this, it was a nasty political fight to get the first ship authorized. SDP overtly ran against Deutschland being built and there was still the echoes of the Zenker scandal. In any event your story. If you are going down this path go hog wild and build 8 PPBs six in service and two in reserve was the German view and UK agreed, France of course didn't.
My thinking is that they are good enough and if they can have four of these instead of the Twins that is a good thing because 4 > 2 even if the ships are less capable because they will further spread out RN assets.
Issue isn't cost is yard capacity, we have no idea what building slips were available in the private yards and the two government yards were taxed. If you want two more units ignore going down the D design path and just build what's actually ready, the design plans for Graf Spee. Neither Cruise D nor Scharnhorst had complete building plans when started. Cruise D like Scharnhorst would have had building delays. Building another two Pocket BBs would have had the building experience to draw upon, look at the building times for those three ships.
6 triple 11" were already on order for Armoured Ships D, E and F, waiting for 15" turrets to be designed and built would have delayed their delivery.
F was never ordered only D and E.
I'm not going to do if in this essay, but I have toyed with the idea of altering the Treaty of Versailles so that the Deutschland class were built with four 15" in two twin turrets to allow the Twins to be built an additional pair of Bismarcks.
Germans considered 15" guns for Pocket BBs the design would have been a Baltic Monitor of 18 to 22 knots. Restrictions on gun size wasn't the treaty itself it was the Inter Allied Commission of Control they restricted Germans to 11.1" guns anything larger at 1 per year. Emden for example was to be built with 4x2 150mm but that design was nixed by the Commission and the result was the historic ship. For reasons of fire control the Germans wanted at least 6 guns and anything larger in terms of main armament and same speed would have been four.
For an odd ball design look up the Zenker BC from 1928. 17,500 tons, 4x2 12", 34 knots and 100mm main belt. This from Admiral Zenker hoping Germany could join Washington Treaty system. Overt cruiser killer and raider.