Today it dawned on me. Why not just store them the way I store all my other leafy greens?
I cut the root end off, cut the leek in half and chopped the halves in half long-ways.
Spread them out on a clean dish towel.
Roll them up in the towel and stick them in a produce bag.
Actually, that is an old bread bag.
Produce is expensive and I HATE wasting food. This method keeps the leaves from touching each other, it keeps them an even moisture all over and it prevents contact with air and will keep your leeks fresh for a week or more and over time save a bundle of cold, hard cash on your grocery bill.
I wrapped these up with out washing and will wash them as I bring them out to use. Some people wash them first when using this method. If you do, make sure you dry them well, because overly wet spots will cause faster spoilage.