This ATL occurs regularly, and while interesting it also rather simplistic imo, like others say, everybody was building new BBs, so imo a more realistic scenario in which the "aviation mafia" in IJN has more sway, is for them to build BBs more tailored to support CVs, that are smaller and faster, cheaper too.
We have the benefit of hindsight of course, but it's fun to play. So one scenario is for them to first, modernize the Nagatos with machinery like Kagas (127,000 HP) which aparently was considered OTL, to increase speed, bringing it at least equal or even more than the new american treaty BBs, thereby increasing the usefulness of these ships. As a side note, does anyone know how to calculate the speed of this ATL Nagato with 127,000 HP, standard displacement being close i assume to 40,000 tons?
Second, built a class of two quick and cheap mini-Yamatos (let's use the same names Yamato and Musashi), a japanese Vanguard if you like, about 45,000 tons, heavily armoured, 30 knots speed, using the guns left over from the Tosa and Amagi classes (24 apparently), so they could have either four twins or three triples. They should take significantly less time to build, no need to enlarge slipways etc., so both might be fully combat ready in 1941.
Third, build two new 50,000 tons heavily armoured fast BBs with nine 41cm/50 guns, these replacing the OTL Shinano and Kii but i keep the names. Because the first two take less time to to build, these two can be started and finished earlier, so they might be combat ready in 1943/1944.
Fourth, instead of the mediocre Junyos, build two proper CVs instead, say one repeat Zuikaku and one repeat Hiryu, it's a much more efficient use of that steel. They both should be operational in 1942 roughly similar to OTL Junyos, but the repeat Hiryu could be ready earlier.
Fifth, bring the auxiliary conversion programme one year early, so Zuiho is ready late 1939 rather that late 1940 with Shoho and Ryuho brought forward one year too. Same goes for the CVE, they could probably get all 3 Taiyos ready in 1941 if they start converting them early enough (that is 1940). Also they could convert the Kamakura Marus as well, so they will have 8 or 9 CVEs instead of 5.
I kinda disagree with the notion that they didn't had enough aircrew, imo the problem, at first anyway, was they didn't had enough RESERVES, so if they focus more on the carrier air airm, they could just train the additional required number of aircrew, but still with the insuficient reserves. They could also skim land based groups for more aircrew, as to the shortage of carrier aircraft, they can for instance have Nakajima build 800 D3A and B5Ns instead of the 400 G3M built OTL, but of course this is just hindsight.