There are serious issues with your ideas for battleships if you assume the naval treaties stand.
You cannot start to build until a Jan 1937 - as was done.
If you are going to modernise ships, for the sort of major reconstructions done you have to assume 2.5 years a ship. Allow for ships undergoing routine maintenance, and you suddenly get very short of battleships at a time international tensions were growing rapidly. This is politically and operational impossible.
Building the ships faster would involve pre-preparing equipment, forbidden by the treaty. The British bent these rules, but to get any major improvements you need to have the government decide to break them (in which case you may as well scrap the displacement limits as well)
Battleship building is constrained by a number of factors, but for Britain it was basically the main armament, FCC, and armour. Speeding up all of these require decisions and money some 2+ years previously. Plant takes time to build, and cant be used for anything else.
There are some improvements that can be made, but unless the government is prepared to spend money earlier, not too much can be done.
(1) Build the KGV with 3x3 15" guns. This was nearly done, this was in the initial designs. Some nameless civil servant decide late on to go to 12x14" guns. By the mid-30's the issues with the NelRod turrets had been identified; with money, these can be addressed and fixe, and then the KGV use the same design. (This would save about 6 months on the construction time)
The gunnery performance of the KGV is little different from any other BB in similar weather conditions - few people understand the issues of trying to shoot a 15" shell on a ship flexing in a moving seaway. The KGV were also as fast or faster than all contemporary designs. Steam plants could have been improved, but again the true power isn't the stated power - plants could and were operated at higher than 'maximum' power, and the lower performance plants could be forced to a higher overspec.
A baby Nelson class would be a poor design. If built, it would be more like a modern Renown, with better armour. Which would btw, be perfect for chasing down raiders and enemy cruisers. Ironically WW2 would see BB's used as battlecruisers, rather than the other way around as in WW1...
They wouldn't take much less time to build, btw - about 6 months at best, even with the armament not an issue(btw, you still have to rebuild the R-class turrets...), you still have the FCC, armour and machinery to build.
One final thing - Tony Williams is excellent on guns - a world expert. He is NOT (self-admittedly) a naval expert, and so except on some gunnery experts his opinion there should be taken with some care.