If you're not already, try using the bridge pickup--that usually helps.
In regards to technique it's kind of hard to describe, after tapping try to pull off slightly towards the floor instead of straight away from the fretboard. This almost has the effect of picking the second (pulled-off) note and gives you a bit more clarity. That way you're not depending on gain as much. If you can get all the notes to sound without max gain, you don't have to deal with as many noise problems.