maybe the pickups/guitar are not as much of a contributor to the feedback problem as you may think
microphonic tubes in your amp may be contributing as well and if you change (or even just switch around) some of the preamp tubes you may greatly reduce the problem
in the OP you stated that you don't have the problem with your strat so that means it must be the PRS but since, using the same logic, you didn't have the problem with the other amp (Marshall?) then maybe the amp is a factor too
consider that the output of the PRS is much greater than that of the strat so the combination of potentially microphonic tubes and high gain pickups may be the issue
you can test your tubes for microphonics by gently tapping them with a wooden pencil (use the eraser if it has one) and listening for a ringing sound through the speaker - sometimes, if the tubes are really microphonic, you can hear the ring just by tapping on the front panel