Dropping players before the first round
A common variation that some stores implement to avoid this sort of thing: draft for “picks”.
You don't keep what you draft, after the play is completed, all Rares, Uncommons, and Foils are collected. The winner gets first pick from the Rares and Foils, then 2nd, etc., until everyone's had a pick - then repeat. If you have multiple pods, you can pair outside pods after 3 rounds, to get a clear winner, or you can keep the picks separate by pod.
Yes, this is legal. (Pre-emptive, because I've answered THAT question a few times, too.)
No, not all players like it this way - esp. not the ones you're having problems with.
Very important caveat, if you do this: you HAVE to explain it to people before you take their money and let them open packs. Some will refuse to play “for picks”; some will refuse to play “keep what you draft”. Both have valid points.
d:^D