[Legate of Amon Lanc]

Interesting thread, elempi. Let me first add one more example from Tolkien that immediately appeared in my mind when I read your first post. It is from the UT, when the Rohirrim guard the Fords of Isen. The situation is somewhat different there, but nevertheless there is probably a reason why I have thought of it.
Briefly about the situation: Saruman's armies were marching to Rohan (and towards Helm's Deep) and the Rohirrim were holding the Fords of Isen. But, after the first battle, Théodred was slain and the Rohirrim were weakened. Other is said in the quote I will provide. Now there were two leaders present, Elfhelm and Grimbold.

Originally Posted by UT, The Battles of the Fords of Isen

Elfhelm held that the Fords were no longer important (...) since Saruman could clearly send forces down either side of the Isen as suited his purpose and his immediate purpose would undoubtedly be to overrun Westfold and invest the Hornburg (...) Grimbold on the other hand was not willing to abandon the Fords. This was in part due to the tradition of Westfold in which he and Erkenbrand had been bred; but was not without some reason. "We do not know," he said, "what force Saruman has still at his command. (...) As soon as he guesses or discovers how we have disposed our defence, he will certainly send great strength at all speed down the road from Isengard, and crossing the undefended Fords come in our rear, if we are all gathered northwards.”

I would say the image of Maldon could have had some influence on this story. Especially Grimbold's stance and the way it's put I could see as negation of the "beorhtnothic stance" (from certain point of view). Especially the way it's put: was not willing to abandon the Fords - due to tradition - but not without reason. Gandalf also does not flee from the Balrog.

Originally Posted by littlemanpoet

Anyway, it seems to me that Gandalf had a few options. He could flee or stand and fight. The Balrog was out of the others' league, so gamely heroism was not an option; also it was outside of the character of Gandalf to go for the chivalric ideal and give the Balrog "a fighting chance". What might have happened if he had fled instead?

That's a thing I always thought of, since it's not clear enough what would have happened had he fled with the others. In the movies, this is taken to the extreme, because the whole scene looks like total nonsense. The way it is portrayed, there is obviously no need for Gandalf to wait for the balrog. He could flee with the others and adios. Would the balrog go outside and pursue the Fellowship? Somehow I doubt it.
I'd say the main thing we lack is the knowledge of the Balrog's speed. Though if he is as fast as the balrogs in the First Age, he could be very fast.