Do Balrogs Have Wings?

[Neithan]

How could anyone disagree with such unassailable logic?

Good God Fordim you can be irksome. You will excuse me, I hope, for taking a torch to your straw man but the example you gave misrepresents the argument.

Having proved incontrovertibly with the above sentence that the great shadowy forms that look like wings are in fact not wings

Notice that Tolkien says that "the shadow about it reached out like two vast wings" not "the two vast wings reached out like shadow" or even that the "shadowy forms", as you put it, reached out. The subject of the sentence is "shadow" not "wings" or "shadowy forms".

we can finally interpret the extraordinarily ambiguous claim that "its wings were spread from wall to wall" as meaning "its great wing-like shadows spread out from wall to wall".

It is not uncommon to refer to something(shadow) by a metaphor(wings) that you used earlier.