It took me a few tries, but I finally got the ring gear installed onto the flywheel. I tried this morning, keeping the flywheel in the freezer for 10 minutes and the ring gear in the oven at 450 degrees for 10 minutes, and that didn't work. Ten minutes wasn't enough.

After I got home from work, I decided to keep it in the oven a little longer, and on my third attempt (20 minutes, 500 degrees), the ring gear slipped on. It wasn't fully installed, so I had to bang at it for a little while, which wasn't ideal (I probably should have left it there a little longer), but it's on there now.

I have conquered the flywheel. I win.