I'm just wondering...what happens if you replace Jarl Balgruuf as part of the Civil War quest before going to Bleak Falls Barrow to get the Dragonstone? Does Vignar simply take over Balgruuf's role in the main quest? I want to make sure I avoid any glitches and whatnot.

I think you have to go to bleak falls and kill the dragon outside whiterun before you start the civil war

No, in such times it only makes sense. Replace and ensure an alliance, and the Nord Vignar will do the same as Balgruuf. J'rahzir is positive this will happen.

From what I've heard, you need to advance the MQ beyond the first dragon battle before Balgruuf will take Ulfric's axe.

Not sure about how early Vignar takes over Balgruuf's stuff, but I assume medsteele is right about the axe part.

I replaced him before the endgame, and Vignar was the one I had to go to in order to trap Odahviing.

Well sorry, but you need the fight the dragon and deliever the stone before Vignar can take over in the War

Silly Kitty's

Ah, yes... Khajiit assumed the barrow one referred to was later than such a deed as this. Tremendous apologies from J'rahzir.