I propose that the team not have any head coach, and that the team be run by a few separate, but equal, branches of leaders.
First, the captains, would be voted on by the players. Three defensive, three offensive, and one special teams captain would be elected prior to the beginning of the season. The captains would be in charge of personnel decisions - who starts, who sits, who plays in specific packages, etc. They could appoint committees, if they choose, so they can delegate some of the responsibilities, but in the end, a vote by those seven captains is needed to approve any decisions on who the eleven players on the field are.
Second, "the bearded one", and "the vice-bearded one", make all playmaking decisions. "The bearded one" is simply the player with the best beard on the team. "The vice-bearded one" is the player with the best beard not on the same side of the ball as "the bearded one". For instance, if "the bearded one" is an offensive guard, "the vice-bearded one" must be on defense. (Special teams players must choose an allegiance to be counted toward.) Neither of the two "bearded ones" can be a captain. The "bearded ones" make all playmaking decisions. Pass, run, punt, field goal, blitz, etc. - all decided by these two guys. The one who is on the field trumps the one who is on the sidelines (hence the need for them to be on opposite sides of the ball). When they are deciding on special teams plays, and their opinions differ, "the bearded one" trumps "the vice-bearded one".
Because beards can come and go, these two players are chosen the morning of each game.
Finally, the recruiters. After the captains are chosen at the beginning of the season, they put everyone in a big room. The captains then line up the rest of the team in a geometrically-logical matrix (for instance, if there are 100 players, they line up 10 x 10; 99 players would line up 11 x 9; 101 players would line up 1 x 101; wait - that's stupid - just stand against one of the four walls of the room). Have one of the captains secretly write down a number, 1 through 5. Then have the rest of the team count off - 1, 2, 3, 4, 5, 1, 2, 3, 4, 5. Whenever they get to the number the one dude secretly wrote down, that guy is a recruiter. All recruiters have to stay after practice and work out your own recruiting strategy. Good luck!
This plan would save the university money, since they aren't even allowed to pay the players. And if you get a bad set of players, it's no big deal because they'll all be gone in a few years - no messy lawsuits like you'd get from firing a head coach.
I bet this team would break records for delays of game, too, based on that first branch.