You should try ramping the pressure instead of making step changes. In the first plot you can see that when you reduce the pressure set point in one step at, 7.8125 s, it reduces the control output by a step too. You must be able to hear or even feel this.
Here in plot ram100 I put in a 1 second ramp for the pressure and helped it a lot. I still see some dip from it but not too bad. I think I'll stop for now until I get some material to press on.
As always you have given me a better understanding. Thanks for the help.