Eh, I'd go the opposite route. You meet a threshold, you go into a lottery. They can all sit there on selection day where the hopper spits out the names of admitted students one by one.
Most admission should be by that route. Set proper threshold and then do lottery. But outright auction for some fraction of admission would be good subsidy for rest. Set minimum at proper level say at least 2-5x normal unsubsidised tuition cost.
