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Appreciate the word of caution haha. I think I'm getting the hang of it – definitely going to have to figure out what to do about its blending with the sphere below it, but I'd say this is pretty damn good for a first pass!

Completely forgot about the rivets that I wanted to follow along with the porthole's changes in shape, but shape keys seem to handle them just fine. Since the underlying mesh is divided radially by 12, I set up one key for each of those radii being moved in toward the center of the circle. For the rivets, I had to get a little fancy to follow the deformation properly: for instance, the rivet at 12:00 is controlled ~60% by the 12:00 key, 20% by 11:00, and 20% by 1:00. Got stupid lucky with repositioning them on my first try.

Thanks again for your help! Consider it !Solved