Now I have been thinking about the problem, and decided that why my first attempt did not work was for 1 of 3 possible reasons.
1) I didn't center that wax ring properly.
2) The wax ring I used was too small.
3) The problem has nothing to do with the wax ring at all.
So rather than rewrite the events of the day they are pretty well chronicled already in this entry. The main differences are that I didn't bother with gloves at all today, and there was a little more confidence (and speed) in taking things apart and putting them back together (and with less mess).-- (and, yes, I still put my head over that hole before plugging it)
When I looked at the condition of the ring I had put on before I thought for sure the problem was option #2, that I used too small a ring, and with renewed confidence I finished the job using a larger wax ring this time.
With great confidence I did a test flush after putting things together again. So, as I asked at the end of that previous post, what happens now when I flush?
Does it still rain in my basement?
No! I can say it does not rain. Now it's a bleeding torrential downpour! I have already got a promise of a loan to cover the cost of a plumber, and tomorrow one will be called.