Could we start by consolidating lineaged pieces? For example, every JF Beach Bum could probably all be lumped together, but users can add themselves as a new source (a separate chain, under one name. That way if there's issues with a couple corals they can still be traced back to a source.) This way labels aren't not just intermingling, but people can request for beach bum 1 time, and one of the threads will give it to them.
Instead of outright deletion of old threads, however, maybe hide old threads and move them to an "archive" folder. Some corals may still be around and it may be useful to long-time members, but I don't think the average user should need to wade through so manydead threads.
I agree with Derek that transportation is the limiting factor. DBTC lockers would have to deal with dips, coordination if frags die (maybe they could be "shared" with the locker on barcode), tank costs, time, etc. Shipping is not exorbitant but still not cheap, most places in the Bay Area cost $15 to ship 2 day shipping, and supplies / packing time and experience are an issue. A DBTC van would be cool but it would take someone's whole day. Not quite sure what the solution could be.
I also think that while incentives aren't the problem, I still think "every x frags given = some prize" could still be a fun mechanic. The prize could be BAR sticker, a raffle ticket at a swap, maybe a t-shirt at 50 or 100 dbtc shared. Doesn't even have to cost anything; profile badges or name colors etc are all options