We might want to get a touch further than we are right now, but at least at the quarter-finals, it might be useful to schedule the matchups and basically have an all-comers approach, with the stipulation that they rewatch (well, once for the bracket, not for subsequent rounds for the winners). It'd just need enough lead time and spacing so that people weren't just overwhelmed.
Otherwise, any approach that gets me into the two films I haven't seen that are left would be preferred by me.