MIMF

I have a Dimarzio super distortion humbucker that wants to feed back at stage volume. Not squealing micro phonics, this is a steady low howl/whine.
Internet searching suggests this is likely the base plate vibrating.
I'm swapping the ceramic magnet out for an Alnico 5 in a couple weeks. Could I stick some insulation on the outside of the base plate to dampen the vibration? If so, would that mess with the sound?
The insulation I have is left over from a hot rod build. It is a very sticky layer of butyl rubber adhered to a heavy aluminum foil. It's used on cars to dampen vibration and reduce noise in the car.
Is this a brilliant idea or a terrible one?

I don't see the harm in trying. I'd probably try potting the whole thing in wax again and letting it cool upside down. Are you using springs or surgical tubing to put tension on the adjustment screws?

Base plate vibration? Doesn't that mean the whole pickup is vibrating? If it's floating in the cavity with springs, I could see that possibly happening. Try a cube of foam under it, or surgical tubing in place of the springs, as David mentions.

I'll try installing it with tubing instead of springs. I'll also try potting it and see where that gets me. Sticking a piece of dynamat on the back is something I could always do in a few minutes.