Prof A and I were discussing this a bit last night, and here is a potential solution that we came up with:
The term intro-prep is eliminated and instead there is just a rule for TEAMS that you cannot make an attack during the first round (as Polarius suggested earlier). This keeps Mayhem from being an issue and doesn't create fuzziness with a "turn" that isn't really a turn. It also maintains the balance of power between getting to play cards first (except attacking) for the first team and getting the opportunity to counter for the second team.
For example--the first player goes first and plays down Samuel and Wheel within a Wheel to grab AutO. He can't attack this first round, but he's all set up to make a strong opening rescue on his second turn. The opposing players can now see that and get an opportunity to play a counter card (say RBD or Golden Cherubim) during their first turn. Assuming they drew a counter (which I grant is not a given) they now have the upper hand because they had the opportunity to react before a rescue was made. Consequently we have pros and cons both for going first and for going second.
With that in place, I feel we could also eliminate the "first player doesn't draw" rule so that the player who goes first will draw first. This makes TEAMS consistent with other multi-player categories. It does shift the balance towards the team that goes first, but since the team with the most souls on the table determines who goes first, that advantage is controlled by them.
I agree with everything here, except the first player drawing. The first player gets the only guaranteed uninhibited shot at doing anything he/she wants without any counters on the board. The first player also gets to attack first. I think these combined benefits are strong enough that they need to be balanced with the first player not drawing on their first turn.
I think this would be ideal:
Player 1 doesn't draw, takes a turn (can't attack)
Player 2 draws 3, takes a turn (can't attack)
Player 3 draws 3, takes a turn (can't attack)
Player 4 draws 3, takes a turn (can't attack)
Player 1 draws 3, takes a normal turn
...and so on.
Under this scenario, by the time player 1 gets to attack, he still has drawn just as many cards by game rule as everyone else. I think it would be too much if player 1 would get to attack first, AND have drawn 3 more cards by game rule than either of his opponents.