I experience the same issue when I started using my 1F (+vfd, pump, vac, etc.) last year on a 15Amp breaker.
I temporarily changed to a 20Amp breaker and did not have issue.
My final solution was to design this which have Dual Power Source (Automatically controlled accessories use a second power cord that can be plug into an outlet that is on another circuit breaker)
Primary power cord for on or off switching of CNC, VFD and Light
Secondary controlled by SSR-Solid State Relay or Manually from switch when position is MAN.