Huge vibration of props until the copter is takeoff

This has nothing to do with PIDs or tuning.

I ran into this with a quad once and the way I fixed it was by shortening the landing gear as much as possible. If you can’t shorten - try lengthening to see if it get rids of the issue. Both should slightly modify the resonance frequency - which may stop vibrations.

I believe the vibration would go away by reducing mot_thst_expo to anything below 0.2 but you claim that’s not. Maybe you should give it a try and tune base on lower value of mot_thst_expo. I had the same exact problem with my alpha esc on a large quad with AUW of 27 kg that higher Takeoff vibration was pretty scary on takeoff.

This kind of vibrations are mostly caused by the landing gear. Not rigid enough it enter in resonance and vibrate in the all frame.