If you are worried about destroying your tone because of digital effects you should be thinking about what that GT-6 is doing to your tone. Think about it, you have a DIGITAL pedal which converts all of your analog guitar signal to digital, then procesess it, then converts it back to analog to run to your Guitar amp (unless you are using the 4 cable method of hooking up your GT-6 which does let you have a amp preamp stage first). Why worry about a noise surpressor when you already are digitzing your signal.
A noise supressor is nothing more than a gate which lets your signal come through when it senses you push it over a certain threshold (when you are playing). So to clarify, a noise supressor will not 'destroy' your tone any more than the GT-6 you already have hooked up.
Don't get me wrong, I have a GT-6 which I mainly use as a backup nowadays and it is powerful..but I am just sick of the distortions and massive volume changes when switching from patch to patch (soundguys hate that). I think you should be looking at perhaps replacing your pickups (which may not be potted). Cheaper quality pickups will squeal like a banshee when near an amp with high gain and volume. You should have some feedback, but not uncontrollable feedback. You may find that standing farther away from the amp helps too.