I recently ran into the other side of the issue with trying to change a reservation from a normal room to handicap accessible.
For an upcoming trip, my mother who needs a handicap accessible room expressed an interest in joining at the two month mark, so pretty last minute for DVC. I called to try and get the existing room reservation switched from non-handicap accessible to an accessible room with roll-in shower, thinking there shouldn't be an issue as long as there haven't been other people booking needing HA since rooms are assigned shortly before one's stay at a resort. Apparently, that's not the case.
According to the cast member I spoke with, the system phantom assigns people to HA at time of booking, so if there is no availability for rooms in general on the website they can not switch between HA and non-HA, whether other members requested the room type or not. To illustrate, if you have a 1 bedroom booked and break your ankle 2 months before your trip, you can't have your reservation changed to HA 1 bedroom unless there is availability on the RAT for all your dates at the resort in a standard 1 bedroom.
I was told the best I could do is put in a waitlist for all 5 nights, and if they became available then the system could reassign us. I did the waitlist, but stalked the RAT and when the next room size up became available I borrowed points in order to get a HA guarantee since it is a race weekend and very popular dates for the original room type.
Not sure that what the cast member said was accurate, but since he claimed to be wheelchair bound himself I think he would be motivated to find out accurate info on this issue.
Moral of the story, if there's a 50% chance my mother may decide to join a trip at some point later than booking, I'm booking HA now even though like a previous poster said, I wouldn't mind getting away from the room type when on a trip sans mom.