This must have probably been proposed many times, but I think the change that could be made in the training regime without creating a different game would be that players should still need 48 minutes at a certain position in order to get full training, but you could set different trainings for each player who received minutes in that certain position.
I mean: if you want to improve your centers' passing, the best way would still be playing them 48min at PG, single training position. But if you managed to get 48 minutes in 3 of your players and 1 of them doesn't need passing, but OD, you could set 2 of them to train passing and 1 OD. Some penalty (10%?) could be implemented if players get different trainings. You should also only be allowed to set different trainings if none of the players that receive minutes are assigned by the engine to that specific position (you shouldn't be allowed to train 2 centers and a PG at PG position, but you could train 1 C, 1PF and 1SG).