Check out WalMart or Kmart and see if they have collapsable wire baskets. They used to have them. I used to own one, but never found much use for it. They are just a wire mesh basket, with a spring-loaded top. I think they may have been designed to retain baitfish or to keep fish alive at a dock, or something like that. They expand when not sitting on something. If they still have them, you could tie the basket off to your boat. Don't rest it on the bottom, crabs might get it - just suspend it in mid-water. Just an idea that came to mind reading your question.
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Tad