I looked at a timeshare once where everyone sent in a priority list for what week they wanted that year by a certain date. Your priority moved up 1 each year until you were first, then back to the end. If you weren't in by the deadline, you went to the back of the line. I think something like that could work for this game.
IE. Have your order in by 9AM, we go in order, and then you can trade what's left from 9AM-11 AM.
Then next round, everyone has until 12:30 to get their order in, and the order moves up one.
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