I've often cut them down to 5 or 10" (they get very woody bases and I couldn't cut any lower) but I don't know how it will work, if it can work, to cut the sides to keep them more narrow for the space you have. Just this past Thursday I was cutting the branching sides of one of mine so I could walk past it.
I think the top branches will compensate by hanging low. We can compare notes by August.
