I'm sure people have offered up similar suggestions, but how about a 2 hour voting window right after DC for losing tribe, where food and water are off limits. The challenge is also off limits.
This counts in the 12 hours, so the losing tribe would then, AFTER the vote, be able to eat/hunt/drink, and do challenge.
This would prevent the Kpell (maybe not ALL kpels, but the vast majority). And also the voted out tanking the challenge.