I speak analog, digital, software and some English.
You say hunting (digital) and I say oscillating (analog). If I have oscillating or ringing I add phase reversal at that frequency. My friends that speak DSP and think time (not frequency) have a word that I cannot remember; sorry I cannot say what they do in this application. I will try in digital. Error amplifiers I make treat errors at the “ringing” frequency (time period) different than errors at a slower frequency. I see I need to get on a different computer and draw pictures.

Change subject!

Current feedback. I have built too many 35,000 volt supplies. They have a potential overshoot problem.
First I worked on the voltage feed back loop and got it as close as possible. This loop has delay and phase delay. 35,000kv=full load, 35,010kv= no load, with overshoot.
Next plot load current verses duty cycle or phase angle (in your case). Example 1A=50% duty cycle and 0.1 amp = 5% duty cycle. Then add a feed back loop with out delay (very fast). If the load is switching from 1 amp, 0.1 amp, 1 amp the duty cycle switches 50%, 5%, 50% in one cycle each. My current loops are not built for accuracy! Maybe the 50% should be 55%. In this case the load starts at 0.1 amps and 5%. The load jumps to 1 amp and the duty cycle jumps to 50% in one cycle, but it should have gone to 55%. The voltage loop sees the small error and slowly adds the extra 5%. When the load drops to 0.1 the very next cycle will be back at 5% with out the error amplifier time to respond. In this example the error amplifier effects are reduced by 10:1.

I have millions of “current mode” power supplies in production where the error amplifiers see only 2% of the load variations. I need to think how to get your supply in truly current mode. Too much for my old head today! I think this is too complex to talk about this way.