I can only assume that after your battery was going dead, and the charging system test (while running at Bulldogs's ...I'm a witness) you have ruled out the regulator/rectifier. While the GS Suzuki's from that era were notorious for frying stators, I hope you have eliminated the reg/rec first.
I sold Mike Beswick a 1981 GS1100 with a freshly rewound and baked stator. He bought the bike for parts and maybe that is part he never used. The stator had less than a season of riding on it before the bike was "retired". Give Mike a call.
Peace & Grease, Dennis