Let's not get ahead of ourselves, and let's be careful about what the text actually says.
Durin's Bane finally died when it was cast off a mountain top by Gandalf
I don't think Gandalf just pushed the Balrog off the top of Celebdil, and that the fall killed it. The moment Gandalf kills his Balrog is described like this: "I threw down my enemy, and he fell from the high place and broke the mountain-side where he smote it in his ruin". I think "threw down his enemy" is a poetic way of saying "Slay his enemy", and "in ruin" means "in his death". So, the phrase could read "I slay my enemy, and he fell from the high place and broke upon the mountain-side where he smote it in his death". Gandalf kills the Balrog, and it falls as a result of being dead.
Tolkien uses "threw down" poetically like this in the battle of pelennor fields: "Right through the press drove Théoden Thengel’s son, and his spear was shivered as he threw down their chieftain" (RoTK, Chapter 6). And he describes both Smaug and Ancalagon the Black as falling in their ruin
after they were killed. So it's not a stretch to think he's using this language the same way here.
I'll admit that it's possible to interpret this passage the way you did. But given how this language is used elsewhere, and the fact that the Balrog just survived a far larger fall (whatever the explanation), I think it's way more likely that Gandalf killed it, then it fell. But, even if I'm wrong, the Balrog
still survived that initial fall. A fall extremely similar to that which killed Glorfindel's Balrog. Why the different outcome? Non-flight capable wings, like a Barnacle gosling's (who sometimes survive their initial fall from their nest, but often don't) is a plausible explanation.
Unless you think Gandalf had a secret wing glider on him?
He totally would have! The Balrog itself would have been his "glider". We know for a fact that the Balrog wrapped its whip around Gandalf as he initially fell ("But even as it fell it swung its whip, and the thongs lashed and curled about the wizard's knees" (TFoTR Chapter 5)). We know that Gandalf was in close proximity to the Balrog as he fell ("Long I fell, and he fell with me. His fire was about me. I was burned" (TTT, Chapter 5)). And we know they continued to clutch at one another after they reached the bottom "Ever he clutched me, and ever I hewed him" (TTT, Chapter 5). It does not, at all, seem to be a stretch that they were entangled/gripping one another as they fell and whatever mechanism the Balrog used to slow its fall to a survivable pace also slowed Gandalf.
The other argument from text for them not having wings is it's stated that Morgoth had no mastery of the skies until Ancalagon the Black.
I'm arguing for wings not flight.
I stand by what I said. The arguments against wings are all arguments from absence. And wings explain the events described better than any explanation I can think of. That's obviously a weak argument. But I think "Wings explain the events we see" is actually a stronger argument than the argument from absence "They're never explicitly described, so they don't exist". As I said, if someone can come up with another plausible explanation for why Glorfindel's Balrog is killed by a fall, while Gandalf's isn't, that tears this to shreds. But the only other explanation I can think of is "some unknown magic did it"... which is both unsatisfying and dull (and has just as little textual evidence as wings).