I think this your idea is fine as a bounty. It's accepted that you can put whatever conditions you feel like on bounties. This would be reasonable to put a a post in the List of bounties with no deadline and link to that, even though it actually has a deadline. This avoids needing to make a new type of win conditions, since each challenge on its own is just normal code golf.
I like in particular the idea of people trying hard on a set of well-vetted challenges. Sometimes it seems like people don't have a reason to golf off bytes rather than just posting quickly.
One pitfall I see is that winning basically requires using all golfing languages. Maybe this is what you're going for, but it's not the type of thing I'd participate in. Even if you can't repeat a language, there's loads of golfing langs to go around. This is especially if different variants counts as different languages, which seems worth trying to make rules for.
It also seems like solvers will want to pair the most efficient language with the longest challenge. Or, to match languages with challenges that they have built-ins for, which might lead to boring solutions. In particular, lots of people might post the same mostly-built-in solution, or be squeamish about posting yet another copy, or be worried they "cheated" by seeing someone else post it.
Maybe you want to have more non-golfing languages. I'm not sure how to enforce that. You could list the languages one is allowed to use, but people might be unhappy being restricted like that. One thought is to use golfing Elo rankings of languages somehow, but it's still hard to balance, and a language's performance really depends on the challenge.