Does recipient have to then offer another item? (I'm OK either way.) If so, I suggest that recipient has X time to to post his item to donate. (Suggest X<=24 hours, or 48 hours.)
Not requiring recipient to subsequently post a donation is more in the spirit of giving with NSA (no strings attached), which, if what I've witnessed of you generous scoundrels in the past is any indicator, won't be a problem for the donors. (I also know darned well that none of you will be too shy to contradict me if I've mis-spoken.)
Other topics for your consideration and feedback:
Trying to do this all in one thread could get very messy. One approach could be to use subject line nomenclature, such that every offering has a subject line that starts with a common opening phrase, followed by a number, followed by a description, which is similar to what was used in the past for the SOL Christmas Family Auction (R.I.P.). I'm not hung up on the verbiage, but here's an example of the structure I just described:
PIF #1--Day Glow Blurple Bet Your Bippy 8 oz. Glider
A separate PIF thread in which donors could claim one or more PIF numbers would minimize donors' posting PIFs with the same numbers (because they're posting at just about the same time). This thread (possible working titles: "PIF FAQs"?, "PIF READ ME"?, other ideas?) would contain the rules of engagement (whatever we end up agreeing upon) as the first post. Donors can make subsequent posts in the "PIF FAQS" to reserve/claim one or more PIF numbers (e.g., from @PSegnatelli, "I'll donate PIF #1" (or similar)).
Recognizing that times are tough these days, might we consider allowing recipients to sell their donated goods if they need to? Perhaps with the caveat that doing so would preclude them from accepting any more donations? Honor system.
Instead of an interval measured in time (e.g., One week before claiming another donation), would it be simpler to define that period in terms of n number of PIFs?