Just cut a section and listen to it over and over and over. That's what I do and I'm sounding more and more like gatton.
Gatton mutes the strings with his picking fingers generally as well his fret hand, unless intentionally palm muting, its sort of an economy techinque so you dont have to move your hand and you can finger pick at will. Its similar to having a skrunchie over the fretboard to quiet down the string noise, except you do it at the other end.
Having fat hands helps as well
