Thanks to everyone for all the great ideas. This actually turned into a pretty interesting thread and I learned a lot from the various responses. In particular, I was interested to learn that ceramics can begin conducting electricity at high temperatures. It makes sense, when I think about it, since ceramics have metals in them. Our furnace is heavily insulated by ceramics, so it could definitely be an issue in the future, and I'm glad to know it.
HOWEVA, in this here case, that wasn't the issue. The wonky Tc was working fine when it was directly connected to a voltmeter. So it turns out the quoted response here was the winner. The PID controller was interfering with the Tc reading through the ground. Lynn was correct that the problem became worse as you approached the PID setpoint (although, interestingly, only if it approached the set point AND was at high temperature. For example, if the PID was set to 500K, there were no issues at all).
Thanks for the recommendation to check the AC and DC voltages between the Tc and ground. The DC voltages between the two thermocouple leads were always steady and as they should be, but at high temperatures, when the PID neared the set point, there was a clear AC voltage which oscillated between 0.5 and 1 V depending on whether the PID was sending current to the heating element.
Removing the ground cable from the Tc DAQ so that all the Tc's are on there own isolated loop solved the problem.
I feel kind of stupid, because it seems like electricity is kind of a mystery to me, but an old labmate of mine used to blame every 'unexplainable/weird' electrical event as 'some sort of grounding issue,' and usually implied that more things needed to be grounded, not less. Apparently that was not the correct lesson to take away : ) . For the record, because some people asked, most of the Tc's we are using are actually just k-type wires spot welded together in-house, in woven fiber insulation.
