Seeing as this thread is kind of a mesh of the suggestions of others, I'll pitch in with one I thought of earlier today. I kind of have an idea for dealing with LP banks, but this really does not help cover any of the other issues involved with claims, just LP banks.
What if, the LP spent into a claim is irretrievable as LP, but remains retrievable as claimed land. To simplify, when you purchase land for your claim, you "pay" for tiles. When you refund your claim, you don't get refunded the LP, but you keep that number of "paid tiles", so that the next time you place a claim, you do not need to pay for tiles until this new claim reaches the area you've got covered in "paid tiles", at which point more LP needs to be turned into "paid tiles". Essentially, you can keep putting in more and more LP to expand claim size. You will never lose the LP spent on expanding, but you will never be able to get it back as LP, only as area covered by a claim.
I've really tried to dissect any issues with this, but I feel I need others with different perspectives than mine to help see if this is a reasonable idea or not, you guys decide.