While I had the Thermal Core out and everything disconnected, I drilled a mounting hole in the tombstone of epoxy around the thermocouple bead, hand-twisting a small drill gripped in a pin vise.

That makes mounting the thermocouple much easier when the MK5 head gets tucked in place inside the Thing-O-Matic case. The washer is smaller than I’d used before, too. There’s no thermal compound under the brick, but I’ll probably add some the next time it comes out.

I pushed the insulating blanket back around the thermocouple and wire, then added a fuzzy button (punched out for the nozzle) atop the mess and taped it all in place. The thermocouple certainly runs a bit cooler than the Thermal Core, but I have no way of measuring the difference.
In any event, I think consistency is more important than absolute accuracy, because you’re tuning the whole affair for best printing at a given temperature, rather than picking an absolute temperature and adjusting everything else to suit.
It’s worth noting that the J-B Industro Weld epoxy in that block was in fine shape, despite roasting at nearly its maximum rated temperature for a few tens of hours. That’s not a lifetime test, but it’s encouraging.