Personally, I would go to a system of rewarding those that attended games the prior season. Anyone that attended all 7 games (themselves) are tier A, 6 games is tier B, 5 games is tier C...4 games is tier D...anyone that didn't get tickets (including freshmen) is tier E...if you bought tickets and attended 3 or fewer games, you're tier F. Do the lottery, and sell them by tier until you hit the sellout, and do a lottery in that tier to see who gets the seats.
It helps encourage attendance, gives priority to those that care enough to go to the games and not sell/eat their tickets, etc.