Look for a cabinet shop supplier in your area & find some baltic birch (1/8") to see how it looks. It's 5' X 5' and fairly inexpensive if you like the birch look. If you go with paneling, I would try to cut it to shape & size first (make a pattern first to see that it fits properly) and do your finish outside on the bench. I wouldn't want to apply finish on a vertical surface ever, if it could be done laying flat on a bench. The ceiling is the same, painting overhead sucks! When I did my headliner, I did it on the bench, glued the canvas in place first, & then put it on in one piece. A bit wobbly, but it was done easier & looks good that way.
If the panels will fit inside the door, tack it up & glue it once it's stained & completely dry with a pin-tacker. That way some simple corner trim will cover the joints, ceiling edges, wall joints, etc. & make things much easier to deal with. If you use trim, there's no need to have completely tight seams & perfect fits. With the panel 1/4" too small in both (all) directions, you really just have an 1/8" gap to cover with trim at the edges.
Not sure about rolling the aluminum. Ask the Amish folks if it will work & listen to their advice. We rolled formica sheets all the time with just a cardboard edge folded over on the end of the sheet to protect it & then used twine to tie it off. Not so sure aluminum would take this type of treatment without bending or folding. I guess it depends on the thickness.