Relocating the strap button on a PRS Santana will make your problem worse. The Chibson SG heel is forward of the very shallow upper horns of that body design, so for that guitar, relocating the button to the heel works, as much as it can. Removing the tuner buttons to test the effect is a fabulous, easy and reversible test. Lighter tuner buttons could affect it. Weighting the control cavity is a cool idea, except that the Santana cavity is very small and doesn't have much room to spare. Just take care of where you try that to not create unintentional grounds, etc. when the plate is secured.
Perhaps the best way to easily address this is to add weight to the bottom end of your guitar strap. There used to be a product called "Heads Up" that addresses the SG problem specifically, but they don't seem to be made anymore. Maybe check Reverb. Here's an old photo:
The other thing you could consider is to take your guitar to a very skilled luthier and have your guitar neck reshaped/reduced and refinished. Even removing finish to a satin feel could be a start, but all of this is not reversible at all except for refinishing, and could be expensive.
Good luck!