Well Boss, you've accidentally proposed another anthology! (Surprise surprise, we do have a board for this).
But yeah, this is basically how the anthologies have worked in the past. Granted, our biggest problem wasn't getting stories to put in the anthology, but finding a place to publish it. Of course it's been years since we last made an attempt, so I'll bet that there are more options out there than there used to be for small scale printing.
I wish you the best of luck! I am certainly down to lend advice and maybe write up a little something something if I can find the time.