Let me say what my code does, and what it doesn't do.
It generates the subsets in the exact order that the original post gave, and does so in a way in which you can easily skip all subsets of the current subset. Furthermore it does this with bounded memory requirements, and with somewhat reasonable performance. However it does not guarantee that it generates all longer sets before generating a short set.
If you wish to guarantee that it generates all longer sets before generating a short set, then you'll have to explicitly remember all of the skips you were asked to make (with potentially large memory requirements to do that), and the skipping step is going to become very complex. Limbic-Region will have to confirm one way or another, but I think I made the performance tradeoff that he would want.