I had the same problem and I turned out the issue was incredibly silly:
I was using a friend’s Russian Big Muff Pi, so I never got a chance to take it home and take a good look at it. It was having the same incredibly random problems you are describing.

It turns out that last time he opened it, he forgot the line up the case/ground wire’s ring with one of the case screws, so it was bouncing around the case, occasionally bumping up against stuff (the output jack in my case).

So whenever you re-close it, don’t forget the ground wire.

I realize that is totally dumb, but I hope it’s your problem because it’s such a relief and easy fix.

Good luck!
-Chris