The past 2 days I have been manually evaluating the resonant frequency of the coil vs. temperature and what temperature the coil settles into for a given core temperature. Currently I am regulating at 1200°C and the field coil is settling in at about 178°C. The epoxy on the coil is only rated to 150°C, but I am not seeing any smoking or softening of the epoxy (of significance). I have relocated the audio PA about 2' farther away from the coil with a longer lead to the field coil. No oscillations have been seen since this change. The resonant frequency of the L-C appears to go lower with temperature, being about 3930 Hz at room temperature and about 3840 Hz with the core at 1200°C. It is more likely the coil is changing frequency with temperature based on the coil temperature going from room temp to 178°C.
Because I have the opportunity to play a different .wav file for stimulation every time it is applied, I am going to create a number of .wav files at different frequencies and choose which to use based on the temperature. Also, the resistance of the coil is changing. At room temperature, a full gain setting produces about 6.3A peak sine wave current while at 1200°C core (178°C coil), the same drive only produces 5A sine wave peaks. So, I will also change the stimulation level based on the temperature.
The coil current sensor has proven to be really useful. I can change the frequency of the input at each manually set temperature and adjust to maximize the coil current to find the resonance. It also lets me see when something is changing or if there is an oscillation.