The "outdoor colonoscopy" should tell me what is going on. A broken
clay pipe, or possible root invasion, is certainly likely. But here is
what puzzles me: why does this backup problem occur only after big
rains? How is the rain water causing the back up? Why, after the
rain stops, doesn't the drain take the water and sewage away again?

I am not planning to dig a 10-12 feet trench and replace pipe. As a
plumber I make a pretty good college professor! I am wondering what
it will cost me to replace, let's say 50 ft of sewer pipe in the worst
case scenario. Any thoughts? I'm guessing $5k.

Thanks for any advice on these questions.
--Don