Have the valves been checked/adjusted?
I think you have more than one small problem building to your situation.
A few years ago my buddy bought a used 660 (I know yours if E.F.I. and all but small engines are mostly the same) that spit and sputtered the first couple rides until the bike was A.P.O.S. and my buddy was about to sell it. I told him it needed a full tune-up, and that he couldn't sell it the way it was so......
The bike belonged to a rancher that probably fill the tank using a bucket and didn't always replace the gas cap between fill-ups.
We washed the dirt from air-filter, removed the gas tank to get to the valves and removed the plug to easily find T.D.C. to check the vales lash.
The rancher had installed the wrong plug, but I keep extras around for a 660.
We adjusted the valves, cleaned the gas tank and pet-cock, installed the correct plug, oiled and installed the clean air filter and put the 660 back together.
The 660 purred like a kitten and we took her for a long ride to test'er out doing this....
Fast Green Convertible "06" 660 on 26" BH OG's with Stock Wheels.
COOP45 Primary, 1.5 mm shim, -1.5 mm belt, Purple Secondary Spring,
21 gram weights, weight covers reduced to 29 mm diameter and a 2 mm Cut Cam Plate.
2 heat range hotter plug, Warn Winch, Passenger Foot Rests, Rock Deflectors, Heated Grips and Hand Mitts,
Grab Strap, Cooling System Up-Grade and multiple position mirrors.
8040 miles, 812 hours on 1-1-15