Tried this, it's really just the side of the transformer that makes any noise when I tap on it, but also, I think I might just be over sensitive. I did an A/B comparison to my audio interface pre and the noise floor was similar to my mp-1. I think I've just been cranking it way too high on quieter sets and back in the studio.
Now that I did a more (or less) scientific test of it, I'm fine knowing that self-noise isn't an issue, but... I'm still a little concerned that I can hear myself tapping on the side of the transformer when the gain is up in the 7-8 range. Maybe the solution is "don't tap on the transformer?" haha