I wanted to get the plane to the paint shop with the cowls on, but I had some difficulty sliding the bottom cowl's right attachment pin through the piano hinge. In the interest of time, I decided to forego taking the cowls over to the paint shop until I could figure out why the lower cowl suddenly didn't fit.
I initially sanded a bunch of the built-up area at the lower corner of the cowl, but that didn't help much.
I later figured out that when I'd painted the inside of the cowls with RhinoLiner, I'd put a coat of it between the piano hinge eyes on the right side. This likely wasn't letting the hinge eyes mesh correctly. I filed away the liner between the hinge eyes, and I'm fairly certain this will solve the problem.