The BMW R1200RT weighs 505 lbs dry, 571 lbs fully fueled/oiled, compared to the FJR1300's 640 lbs fully fueled. And the RT is also a fully-faired tourer with adjustable windshield, shaft drive, and a 7.1 gallon gas tank. The engine's a 1170cc two-cylinder, which is likely largely responsible for the lighter weight.
Buells use a 1203cc V-twin and they weigh 395 lbs dry. Of course they're naked bikes.
More food for thought: The Concours 14 has a wet weight of 670 lbs, but the ZX-14, which uses the same engine but has chain drive, a fixed windshield, no side bags, etc., weighs 567 lbs wet. That's about 100 lbs lighter. Of course the side bags alone probably weigh 30 lbs or so combined.
Anyway I think the biggest problem is the engine. Perhaps a two-cylinder would allow for a narrower (more comfortable) and lighter bike. Relocating at least some of the fuel under the seat would also be beneficial.