Here I'd suggest instead to eliminate the rank requirement, as long as we keep the merit requirement and have the merit requirement set to 30 instead of 50. Regarding abuses, again, chances are very low: who would make some merit abuses to merit his accounts from a possible own accounts farm, in order to have 50 earned merits per profile just in order to participate at a pie making contest?
Tl; dr: my suggestion is to
extend voting period to 2 weeks, set an eligibility rule allowing
only users which earned at least 30 merits and 30 activity (no matter the rank),
forbid merit sending from nominees to those which voted for them; and
allow eventual sponsors to hold their funds and personally send them to winners

I agree with you on all you just said, but I would have love to make an alternative suggestion that how about we lower the requirement a bit more by saying that to be eligible to participate in this contest, a user must have at least 10 merits & 30 activity, since that's the least criteria needed to take part in most signature campaigns (I.e Member rank), as that will give room to more contestant and voters. While the voting period remains at 2weeks.