Can I use the action window between staging and quest resolution to exhaust Asfaloth and clear out one 2-point location from the staging area before its threat is calculated? I've always played it like I can, but recently I did wonder. Galadriel can add her willpower last second before the questing is resolved, so is Asfaloth capable of acting in the same "space"?

Yes, you can.

That action window before quest resolution is the best time to play Secret Paths, Radagasts Cunning, trigger Asfolath and all that stuff.