What follows is my personal opinion and not policy... (i.e. before doing anything see how the votes on this or any other answer plays out, to gauge general community consensus)
I have seen questions asked on the main site in the past that effectively constitute "contest" questions and they've been closed as too broad. This is strictly true under the current policies and I don't think you'd have much luck taking that approach.
That being said, we also have precedent for "open ended" bounties here on meta, and we similarly have precedent for topic challenges and other community "events", so I think there's still wiggle room to work with.
So, if this were to work, I think the way to go about it would be to create your "challenge" post here in meta, stating your contest restrictions and proposed deadlines/prizes, so that participants can post their entries as unique puzzle posts (each individually following normal site rules). People could then post on the meta question ...i.e. basically make it like a custom version of the normal fortnightly topic challenge.
Two challenges/problems I foresee though:
- You may get some community resistance because it arguably competes with the existing FTC process, which is more democratic
- You'd receive no bounty from your question to pass on to the winner, so you'd have to find alternative ways to "fund" it*
My personal opinion is that we should absolutely support this sort of community activity, so I'm all for it (under the FTC-style structure described above).
* If the general idea gets community consensus, and I personally find the contest topic interesting, I'd be happy to contribute to the prize pool.