First of all, increase the roster size to 80. While not 100% necessary, this would be nice. Although I don't see it happening this gen, since they already decreased it from 70 to 69. More players would make the new offseason more realistic.
The new offseason should be much like it is now. The difference being training progression is done behind-the-scenes and we don't get to see the results. We also don't get to see the incoming recruit actual ratings (we'd still know the letter grade ratings from the current recruiting model).
All the incoming recruits and returning players are available to play in a spring game/summer camp combo game, like someone suggested. Although not true to reality, that would probably be a better idea from a video game perspective. All the incoming and current players would go through a single evaluation process...less tedious for the programmers and us players.
We set up a pre-game depth chart, which is only used for the game. It doesn't impact a player wanting to transfer. The spring game should play just like a regular game. Choose to play offense or defense. Maybe coordinators can only play their side of the ball. We can adjust in-game depth charts, sub players. Injuries can occur if on (hopefully medical redshirts are re-added).
After the game, you get one chance to set your preseason depth chart, still only knowing pre-progression ratings (last season's actuals for returning players/transfers, letter grades for recruits) and spring game stats. This way you should be basing your chart off of in-game performance and projected ratings.
After the preseason depth chart is set, you then see the actual progressed ratings for returning players and number ratings for recruits. Depending on how you set your chart affects players wanting to transfer, Ex- if you put a 76-rated CB over a 90-rated CB, it would increase the 90s desire to transfer. This info can be stored and used in the current players transferring model. It could also affect player promises. If during the season, you move the 90 back over the 76, the 76 would have more desire to transfer.
Then you advance to the current preseason model, except Set Preseason Depth Chart is removed. Then play out the regular season until the next offseason.