The muffler's fiberglass tube, that connects to the exhaust hose, developed a crack. Here's a picture of the tube.
Clearly visible, thanks to the carbon in the exhaust, is the line of failure. The line was along a seam in the fiberglass layup. I suspect that's why the tube fractured the way it did.
The line of failure and the area around it was cutout with a 1/4" wide abrasive wheel.
Tape was temporarily put inside the tube along the length of the slot. The slot was filled with West 404 thickened epoxy. A layer of mat and cloth, wetted in West epoxy was wrapped around the entire circumference of the exhaust tube.
After finishing the rough edges, the exhaust hose was reattached to the muffler.
An eight hour run, at 1800 rpm, confirmed that there are now no leaks.