I believe the agent will "own" the booking after it's ticketed until you fly the first segment, but for now I think the space is yours to manage as you wish. (The experts can correct this.) I suppose your TA might be miffed at losing the commission, but it seems to me that you've been trying to get this thing booked for two months or more, with frustration after frustration. I suggest you use one of the suggested paths to get the tickets in your pocket; if the TA whimpers about it, explain that you thought you were doing him a favor by lifting an obviously unpleasant burden from his shoulders.

Then see if any of your compatriots can recommend a better TA.