I note that the "Average Power" trace on the streaming coverage of the replication is currently (Tuesday Apr 10, showing temperature cycling between 500C and 800C) much smoother and more in line with my expectations of a 5 minute moving average than it was previously during the ramp. Not sure why.
Under the cycling regime, the temperatures really never settle, so the PID is always trying to catch up with the thermal settling time, and the sign of the differential (the "D" in PID control) only flips as the cycle reverses. The result is relative absence of servo hunting and a smoother curve.
We will soon change from 1 hour to 15-minute cycling interval in response to advice received by BobG from LION.