Here's a new thought that I certainly haven't heard: Shape-shifting.
Beorn in
The Hobbit was able to change completely into a bear. A Balrog, presumably a more potent(I use that to mean having more power of spirit or
Fea or might, whatever you want to call it) creature than Beorn, could very plausibly 'create' these wings at need and then simply 'uncreate' them to fit into a tight spot. I mean to say that he would simply push his shoulders out to make the wings and then the Balrog would simply shed them away. And since shape-shifting was not unheard of in Middle-Earth, this could easily have happened.
Now, I know you are all shouting 'but a Balrog is stuck in that form!' Well, who's to say that it couldn't slightly alter its form? I mean, what difference would this be from say, reaching out with it's arm? It simply extends part of itself; stretching out sideways, if you will.
Well, I think it would work.

I'll just sit back now, and let you all ridicule me for my strange possibility.