[ActionMaxon]

I could see how a bent prop shaft could eff the transmission since it would essentially be shaking things up.

But a bent propshaft would be giving you symptoms driving at speed, not just slowly backing out. Maybe if it was a bad u-joint? Not sure.

I guess if it's all being covered under warranty let them do it, so long as you trust their work. I would ask for a thorough explanation of how they came to their conclusions.

It does sound like you are their lowest priority given how long they have been taking. Removal and replacement does not take long, so multiple days doesn't make sense unless they need to wait for parts to be delivered.

Anyway, if they keep dragging their feet just call every day for an update until they get the hint.