"...it's not efficient to have a half-dozen folks chasing after a reward (large or small) when only one version of the work's going to be accepted. Is there some way to put together a fair process so we don't have folks duplicating effort yet give everyone a fair chance to participate in paid work of this sort? Keeping the amounts modest helps in that not everyone will fall over themselves to do a week or so of work for $400..."
You may wish to check out my article The Wall Street Performer Protocol: Using Software Completion Bonds To Fund Open Source Software Development. It's dated, and long, but it may spur some ideas for allowing developers to get paid, without interfering too much with the development process. It offers one possible solution to the problems of a) wasteful duplication of effort, b) properly identifying and rewarding those who contribute to the work (including non-programmers), c) allowing those who cannot/will not code to signal which features they would be willing to pay for.