Does the order in which you finish Broken Age (Act I) affects the ending?
Solution 1:
It doesn't seem to: (skip to around 16:00)
I finished the same way you did, but this walkthrough shows what happens if Vella finishes first. Seems to be exactly the same, just in a different order.
I.e., each character's fainting is where they leave off, and then both rejoin for the final cutscene.