I imagined this as a version of the "Box O'Crap" game with slightly different rules... but you can work it any way that works for you.
Post a frame you don't want. Hope someone posts one you do want. Two-way trades, three-way trades, fifteen-way trades, whatever you want. But all parties should agree to all stages of the trade before sending anything.
My submissions... deleted. I gave them to friends.
Edit: We now have a SPREADSHEET giving the dimensions of a frame that would fit, and going into some detail about the frame(s) we're hoping to be rid of. I didn't make the spreadsheet, we have Dashuaigeh to thank for that. SouthPawBoston tweaked it a little. So did I. Suggestions are welcome!