How about raising the bottom up to the level of the current surface, then building a mound around and over the whole thing?
Not gonna work - the pit is basically UNDER the shed - nowhere to go up.
Spoke with the folks at the local hardware/lumber store, and they came up with the idea of an extended drain trench, with a tube feed from the drain fitting. Worth a try and easy enough to implement with a trencher machine (which I was getting for a weekend anyway for some other work)