Now that's more like it!
I opened up the guts of my Skutt cone 10 kiln today to see if I could bring it back to life. After unscrewing a few things here and there, I found the issue to be a worn-out thermocouple. Of all the things that could be wrong, this was the very best option. I replaced the part, screwed everything back together, reloaded the kiln, crossed my fingers, and started it up again. Now, 8 hours later, the kiln is nearly finished with the glaze firing cycle and I'm feeling at peace with the world.