Hi Torten,
In your ATL, you want 3 small Yamatos, two Hiryus (instead of OTL which ships, Nisshin and...?), and one Shokaku instead of OTL 2 (is the Zuikaku replaced by a Hiryu?). Would appreciate some more insight into your ideas. Nisshin could be replaced by a Hiryu, yes, though not sure how to get 3 small even Yamatos built at the same time as there were only 2 slipways capable to build BBs in 1937. When i have time and the disposition i always like to ponder about things like these (japanese wiki is very useful and enlightening sometimes), i hope i am not mistaken but i am pretty certain that chart is wrong in some places, Shinano was built in a brand new slipway (the third capable to build a BB, built between 1936-1940), which it occupied until it's eventual launch in Oct. 1944. It appears that the slipway where Shokaku was built was then used to convert Zuiho, Shoho and possibly Ryuho, while Unryu, since it was planned anyway before the war, was only accelerated after Midway, though i can't recall now if it followed Ryuho, or it was built in yet another, separate slipway. But again, better check japanese wiki on shipyards.
Anyway, as to getting smaller Yamatos, it's relatively simple. Have the political leadership (Army?) decide - through a decent, plausible POD, can't be that hard - that Japan is better served if it sticks with the WT size limits even if discarding the numerical limitations imposed on Japan. Another poster pointed out that on 43,000 tons you can have a nine x 41cm ship able to do 30kts. It sounds perfect for this ATL, hell, have them build an L/50 41cm gun for it so you get something more formidable than anything the americans have until the Iowas.
As for an extra one or two carriers compared to OTL, getting pilots of them is again relatively easy, the IJNAF had i think about 4000 pilots in 1941, mostly for their shore based units. Have enough of them retrained to fill one or two extra carriers, sure, this might butterfly a handful of landbased fighter and bomber/attack units, but nothing impossible or improbable.
Btw, i also found prices for various classes of japanese ships, from memory a Hiryu or Shokaku would be about 80-100 mil yen (varrying a bit with year/inflation/type), a OTL Yamato closer to 150 (but would be a bit less for smaller ones, maybe 120 mil in 1937?), 60 mil for a heavy cruiser, 30 mil for a light one, 12 mil for a DD etc. The Junyos together cost 114 mil yen, so aprox 57 mil per ship. Figures for the IJN budgets before WW2 can also be found.