Bruva a new 2nd hand one will cost you $50 at wreckers and yes you have to remove the door card to install another mirror.

Its very simple to remove the door card on Honda's. I think there are two screws one on the handle that opens the door and one on the arm rest. Rest is clipped on. Then remove the wire for the auto window switches and dont forget to unhook the lock latch at the back. Seriously will take like 5 minutes or less to remove the door card.

Dont bother fixing that motor when a whole replacement part can be had for this cheap and would take 5 minutes to swap it in.