Re: My SG is "Bottoming Out"
Ok, re-reading the initial post, you're comparing apples and oranges with regards to these other instruments and their resonance.
First, if the guitar is going from feedback to squeal instead of silence, it's the potting of the pickups. Once the note dies, there should be silence. If it's resonating enough for feedback to begin with, it's doing what it should.
2nd, if this issue is limited only to feedback turning to squeal, perhaps you're using the wrong guitar for the type of music you're playing on it where you require excessively long periods of feedback. If open and fretted notes otherwise sustain normally for the acceptable use of most musical forms, the guitar's weight is not the problem.
Is this the only short-scale guitar you have? If your technique is predominantly focused on making heavier 25.5" scale guitars do their feedback thing, perhaps you're expecting it to behave like a heavier guitar with a longer scale, when it's physically limited from doing so.