We've got a small (12" diameter, 10" high) cylinder-shaped
study/library in our house that we'd like to paint an Old World
Italy/Mediterranean map on the ceiling of (if not already clear, she's
Italian, which also gives some insight into why I never have much luck
arguing with her on these crazy ideas . Ideally the map would be
given a textured and aged (faux) appearance.

I was wondering if anyone could offer ideas or experience on how this
might be done? Perhaps save some neckaches by painting onto one or
more stretches of canvas then adhering these to the ceiling, then
painting/texturing over the canvas to give a seamless and aged look?
Or would it be better to paint directly onto the ceiling, e.g. base
color, then texture, then paint the map last?

**She's got quite a few artist tools that might be helpful -- lots of
unstretched canvas and an image/photo projector that could project a
map onto the ceiling to use as a guide for painting.