[Leec]

This might sound flippant, so forgive this if you've already been down this road, but just slow down and practice. Pick exercises that typify the type of phrases where you're getting a lot of unwanted noise, and practice them with a decent amount of gain (i.e the sort of sound you'd like to use but hitherto are unable to due to exessive noise) slowly, watching and moving your fretting and picking hands carefully, see where the noise is coming from.
Try to correct the problem, and speed up.

I used to make a lot of unwanted noise with my alt picking because I had sloppy technique. Once I got into Rock Discipline and took things slowly, got proper technique down, it stopped and I was able to progress without the problem of noise.

Like I said, you may have already exhausted this approach and simply can't fix it alone, in which case, getting some help with a good teacher who can actually see what you're doing might be best . It just seems a little daft to persist with the problem of making noise and then try to invent a mechanical solution to that. Try to treat the cause, not the symptom. Ockham's razor, man!