The Japanese studied conversion schemes for all ten of their older battleships after Midway. Initially, these were full-scale jobs, involving removing all superstructure, main batteries and heavy/secondary guns then adding a full-length flight deck, island superstructures, offset funnels and AA batteries. Airgroup was estimated at 54.
The Kongo's were ruled out because they were the only big-gun ships fast enough to act as carrier escorts, the Nagato's because the IJN did not want to lose their 16 inch guns. Eventually surveys showed that rebuilding the remaining four battleships was not viable; the conversions would take at least two years and would consume more resources than building carriers from scratch.
That left the idea of rebuilding the four 14 inch ships as semi-carriers. Originally, it was planned to rebuild all four ships (they were very unsatisfactory battleships; the distribution of turrets along the ship's length gave an awful lot of magazines to hit and the 1930s rebuilds had been carried out without proper structural analysis causing excessive stress). However, shipyard congestion meant that only two battleships could be converted, so the Fuso's were dropped from the program.
The reasons for the selection of the more modern Hyuga's for the conversion were mostly gunnery. The Japanese had increased the elevation of the ship's guns by deepening the gunwells in the turret rather than raising the trunnions. Hull depth aft had prevented this for the aftermost turrets so they had severely restricted elevation, at long range reducing the gunpower of the ships by a third. Also, Hyuga had had a turret explosion on 15 May 1942 that had destroyed X turret - damage that still had not been repaired. Although Ise and Hyuga were slightly faster than their older cousins, the difference was not enough to be really significant.
There were a lot of competing plans for the conversions, including some that would have removed four turrets rather than two. In fact, the simplest and least extensive was chosen. Analysis showed that the ships could only use one catapult at a time so any airgroup larger than 24 aircraft could not be efficiently launched.
The conversion saw the removal of both aft turrets (weighing 864 tons each) and both barbettes (another 800 tons). In their book, Layman and McLaughlin claim that the hangar deck/flight deck/catapult assembly weighed much less than this, leading to a dangerous increase in metacentric height with the resultant danger of very rapid rolling. This, they indicate was the reason why the aircraft deck was covered with an 8 inch layer of concrete, reducing the weight loss to 600 tons.
Personally, I would argue this. I believe that the concrete was put in there to correct a trim problem - the nearly 2500 tons lost was at the end of the ship's moment arm while the flight deck was weight distributed over a significant proportion of the ship's length. Shifting weights around like this is no small matter - even apparently small changes in weight distribution can have unpleasant and unanticipated side-effects. My guess is that, without the concrete additions, the ship would have trimmed badly by the bows with a very serious impact on speed.
The concrete would also have stiffened the ship aft, replacing some
of the structural support lost by removing the barbettes. All four Japanese
14 inch battleships were structurally weak, anyway, so reinforcement would
have been no bad thing.