I've probably been away from pistol shooting for ten years. Now that I'm back, I've got a new problem. I normally wear progressive lenses. I find myself having to tilt my head way back when trying to get the rear sight in focus. That's not comfortable. Do I need a good pair of reading glasses, or is there some other way around this?

I've been there, done that, but I didn't wear bifocals, which is what I assume you mean by progressive lenses or similar. At any rate, I think, besides red dots or scopes, you will find that if you drop back a step or two from your "reading" lens powers, then you will be able to see the sights reasonably well while having a fairly blurred target. If you're more serious than that, you'll probably need to go to your eye doctor and explain the problem (bring a pistol).

Maybe I should pop the lens out of one side of my reading glasses.

That would probably give me a throbbing headache, and a good number of misses.