Thanks, Pipe Down. The reason I didn't just compare (shim) it to the
frame is because the lauan is at the top of a steep flight of cellar
stairs. While I can manage (and have repainted and rehung) the lauan
by myself, the solid wooden door is too heavy for me to handle alone.

Method 4 is the most logical. But what did you mean by measuring the
diagonals? Particularly because the cat door is paneled (that's what I
meant about mullions and stiles perfectly perpendicular to the floor),
I think this "issue" may be pertinent.

I just thought buying a new door would reduce stress in case something
in the original door got destroyed! I tried to come up with a
professional method of cutting an upside-down "U" shape with my
circular saw and jigsaw, but it got pretty messed up, and I'm going to
make liberal use of duct tape and padding so the cat won't get hurt.