Yep, I cut it a couple of inches below where the rot was showing, and the cut end looked and felt solid. Then treated the stump with some hydrogen peroxide, and dumped cinnamon on it.
My order of Thiomyl (the generic form of Cleary's at about 1/3 the price . . . ) arrived today, and I also got some Daconil a few days ago, so I am now 'armed and dangerous' as far as fungicides go. I hate using chemicals, but am just over the top with battling the black rot and leaf spotting diseases.