After thinking about it for a bit, I decided that if I’m building an airplane, I’m going to do it right! I just didn’t like how the door was sitting in the opening, so I drilled the hinge out and threw that hinge half away.
I grabbed some extra hinge material I had around and cut it to size, joined it to the door, and redrilled the hinge to the door opening again, this time being extra careful with two things. First, I pulled the door in a little more than last time. The second thing was that I was more careful with the gap between the hinge eyelets. There is a little play between the eyelets, and if you don’t account for this when you are fitting everything, the door will sit low in the opening.
This time, I think I’ve got it just right.