I know this may be easy to suggest and far more difficult to actually put in place, but it would be a great idea if when a player's team was playing a doubleheader they were able to be adjusted per game, and given 2 separate drop downs and it was treated like basically 2 totally separate games/days.  Often times hitters don't start both games and when you slot them in you can lose a game because of this, or even worse a game can be counted simply because a player came in for a defensive subsitution (which gives me another idea).

For example if KC is playing the Twins in an upcoming doubleheader.  What if I only wanted to play Justin Morneau (for example) in the 2nd game against a right handed pitcher, but not against a lefty in game 1, I should be able to do so.  I should be able to select bench for 1 game and not the other.

Or, what should also be able to take place (in a perfect world I know) is that you're given 2 slots and it's like 2 totally different days (to be treated), like I can play Morneau in the day game against a righty, choose to then bench him for the night game, but insert another 1B for the evening.