What I found interesting, and what doesn't appear to have been picked up on (although admittedly I couldn't bear to read the whole thread) was the quote "With a terrible cry the Balrog fell forward, and its shadow plunged down and vanished".
The key point here is the difference between "fell" and "plunged".
What we have is a shadow like wings, which seems to be detachable from the main body of the Balrog. Remember, here the Balrog is only beginning to fall forward, whereas the shadow is already well down into the depths.
So I voted "no".
Wings, definitely not.
Jetpacks, now that's a "maybe"...