Swap out your bridge Seth with an A4 magnet. Easy to do if it looks, scary, it is not. I play Sitar, and on the sympathetic strings, the physics talked about here do not apply. I can't argue why as I am not a student of physics, and I get the point, but if I hit a D on the playing string, the 3rd,5th, and 2 other low D's, and high D,s ring out in sympathy, they are on a small bridge under the huge playing bridge. If I go to 8's, there are too lax and don't ring out as well. Here is the rub. If I go 10's or 11's, which I have tried to get more sympathetic ringing, it does not work. They make a sound, but they sustain clearly less than half as long as the 9's. Go figure. I was sure the 10's would work.
I do agree that seems odd, and the idea that physics would force the string to respond differently, louder and longer, but they just don't. Hit your A string hard and only stop the A from ringing and you will hear sympathetic sound from the low E and D strings. That is what a sitar does, only louder (too long to explain why)
I say 9's or 10's, and THIS IS VERY IMPORTANT- VERY IMPORTANT: My old LP has the screws for the thumbwheels directly INTO the wood. On my SG 61 RI the screws were these fatter ones that screwed into a NEW metal bushing that had been drilled into the body. I took the bridge off and the "New Housing" was loose on the guitar body. It wiggled for gods' sake, so I cleaned the finish off that was all over that metal-took it out (look out for cracks) and put some chopped up maple and rosewood into the new hole that is NOT on any of the earlier and sought after Gibson's. Only the $5 thousand dollar and up Les Pauls' feature the real thumb wheel screw attachment. Then I put the bushing back in, and I needed to gently tap it into place and it was now very firm and helped the sustain greatly. Also -on this Stop tail problem. All my Gibsons' touch. As this bridge is replaceable, I just used a small rat tail file and made room for the string to travel more smoothly and even not touch the back at all, because having the Stop bar all the way down is very important. Wrapping over the top is better than nothing, but having the bar down tight and having the stings hit the bridge at that greater angle will also make a world of difference. I wish I could come to your house and show you, use my parts on yours to prove I am not making this stuff up. Look at a new SG or other new Gibson bridge thumb wheel screw set ups, then look at the older Gibsons or the re-issue $5,000.00 and up thumbwheel set up. They are 2 different beasts.
Steve-seriously