I had a similar problem, but it wasn't as well-developed as yours. Since I work in the electronics industry, my failure analysis would say that the heating wire got broken from repeated flexing via contact from the metal bar and stitched leather (see second photo). Over time, individual strands broke one at a time, until it developed a hot spot because all the current was being carried by fewer and fewer wire strands, until there were no strands left. The burn marks are from the last moments (but could be as much as hours) before it failed completely.
I was able to cut out the burnt/broken section, and solder in a short piece of 22AWG fine stranded wire. I don't have a picture of the solder rework, since all I did was cut out the burnt part, stripped off the plastic insulation from the existing wires (I used the 26AWG slots on my T-Stripper), and used plenty of liquid flux to help with soldering.
Instead of hog rings, I used a trick I came up with a few years ago for fixing broken buttons on furniture and mattresses - zip ties.
This is before I cinched down on the zip tie:
I still had to take half the seat apart to find the broken heater wire, and this picture was on the way to buttoning everything back up:
Total repair time was under 3 hours. And I saved myself at least $90 in a replacement heater pad.