The driver's seat had some damage (dog left in the car while the guy ran into a store...) and the seat heater wouldn't work. I pulled the seat out of the car.
The big chore to tackle was removing the doors.
The front door didn't open from the outside (but could be opened by climbing in through the passenger seat and unlatching from the inside.)
It turned out that the read door didn't open at all. The impact of the deer appeared to have smashed the release mechanism for the door latch. Even when I removed the interior door panel, there was still no way to open the door.
So, I cut away at the outside of the door, was able to get at the latch itself, and manually release it. I was then able to completely remove the door.