My '50's Gibson LG-2 is having what sounds like the same problem repaired right now. I had tried making bigger bridge pins, tried wrapping masking tape around them, tried wrapping & gluing light sandpaper around them...all to no avail. Finally a good repairman figured out the problem. The holes in the bridge plate (under the bridge) had become too large. The repair is to either replace the bridge plate (easy if it pops out without too much trouble), or add a thin 2nd bridge plate under the original one (if the original one is too firmly glued in).

The damned things can hit you in the eye when they do their missile thing.

Halfblind Mark Roffe