One way to look at your problem is that it is less of a heating issue and more of a heat loss issue.
We have several 2'x3'x12" RBI cages (with UTH and 80W RHP) that are stacked in front of a large window. We live in New York and in the winter we have to keep the curtains closed. If we don't, the heat loss through the window is so great our that we run in to the same problem you are experiencing. And you've got an extra foot of caging to deal with.
My advice is to try to reduce heat loss. Try covering one or more sides of your cage with foam insulation and see if that helps.
A side benefit of reducing heat loss is that your RHP won't have to work as hard and you'll save a few dollars on your utility bill.