I'm going to say that nothing's impossible, but in an AD, it will be difficult. One of the problems is that the access is so very tight inside the door. You've just pretty much got one hole way in the bottom. But what I've seen a lot of hotrodders do is cut out the inside steel panel of the door, restore the innards, and then have a nice upholstered panel made to go over it. You could do the same.
I restored my windows the hard way, but the steel inner panel is not sound-insulated, so I've been thinking about getting a panel upholstered for my doors too.
