I loathe garbage disposals- more trouble than they're worth. As you discovered, a jammed disposal is a lot bigger deal than a regular clogged sink.
It would have been more expensive but less time consuming if the problem had been in the disposal. No, the clog was at the end of a 25' snake.
It looked like this:
1) disassemble P-trap
2) send snake down drain pipe, maneuvering snake tortuously through several bends
3) find clog and work snake
4) withdraw snake and remove nasty stuff from auger
5) return to step (2) until can't pull more clog out, typically three repetitions
6) reassemble p-trap
7) send water down drain and wait for disposal and sink to fill
8) observe and discuss with daughter how fast or slow the water drains
9) return to step (1) -- probably a total of 25 times altogether
Add to that misidentifying the drain pipe downstream, cutting the misidentified pipe, rodding the misidentified pipe, and sweating on a $30(!) tee to make a cleanout where one was not needed. Not to mention repaying a gigantic favor to my friend who did the cutting and the sweating.
Looking on the bright side, that cleanout may come in handy one day. I now know for sure where all the pipes are in my house. I learned enough about sweating copper pipe that I could do it myself next time, I think. Middle Daughter volunteered a lot of her time to hang out with me and learn about plumbing. The friend who helped me is getting a free pistol class with me. And, of course, from now on when we go around the table at Thanksgiving to talk about what we're thankful for, I will always have something at too of mind to say.