Not exactly the same issue, but I have been experiencing the surges and slips you describe - one minute spinning, the next a resistance āspikeā to the point I can hardly turn the pedals. Also, unrealistic power estimates. Wahoo Kickr Core + PC + Zwift Click. Itās driving me round the bend, and have been seeking help for about a month now, with no solution at hand.
If youāre not using virtual shifting, it may help to turn it off manually in your preferences as explained at the link below. I was having a similar problem and it worked for me.
P.S. There is now a switch to turn it off in game, but it would automatically reset itself back to on in the background after each session, so I found manual shutoff was necessary.
In that case I would encourage you to perform manual spin downs in Wahoo app frequently (once a week-ish). Something about Wahoo auto calibration and Zwift virtual shifting didnāt seem to play well together to me. Before I turned virtual shifting off, I did this and it seemed to help.