those are all great methods to stop the trem springs from ringing -- i use a thin strip of foam between the body and the springs -- but i've never heard of springs causing feedback like you describe. vibrating springs usually give a faint echo like reverb when you suddenly stop playing and mute the strings. feedback comes from the pickups.
the "wom" sounding feedback you describe, a low moan rather than a high-pitched squeal, usually comes from the pickups vibrating in their mountings. it can happen when the strings are muted [just like ringing springs]. to see for sure, get your axe feeding back and then grab the pickup really tightly between your thumb and finger. if it's vibrating in the mounting, you should feel the vibrations and your grip should choke off the feedback.
this kind of feedback can be really tough to fix -- since it's not loose windings vibrating inside the pickup, repotting the pickup won't help. on Les Paul type humbuckers mounted on rings, i will stuff a huge block of foam underneath the pickup in the cavity. with the 7620 direct mount, you can't do that. you could try bigger mounting screws and more strips of mounting foam underneath the pickups.
a first check would be to make sure the existing screws are clamped down tight. if they aren't because you've got the pickup set high, close to the strings, consider adding more mounting foam or thicker foam, so you can have the pickup high yet still crank down on the screws.