SeaFoam will dissolve varnish pretty handily, but only if it is not plugging any jets. Did you overhaul/clean the carbs yet? Try the
SeaFoam, first, as it is the easiest. If that doesn't help, then pull the carbs off. I've had a few friends use it in the gas tank, with great success. It is a minor miracle, sometimes, other times, it does nothing noticable. It is inexpensive, and easy to use, though.
I would recommend running it through the gas tank once every 45 days, or so, just as a precaution, to keep ahead of the varnish deposits in the fuel system. Ethanol gas goes bad, according to some articles posted on the Internet, after just a couple of weeks time. It will only reduce your mileage a little bit, but if it scours the fuel system, avoiding more severe problems, it is worth your time, and money.
I would recommend
SeaFoam in the crankcase, as well. Add according to the bottle's directions. Run it on the center stand for five minutes (if cold), shifting through all gears, letting the rear tire spin with the engine
idling only. After five minutes, the oil will be around 180 F. Check its color, before you start, and after: it most likely will turn jet black after five minutes of running with
SeaFoam in the crankcase. This will be carbon deposits, varnish, and other sludge the
SeaFoam will have dissolved within the engine, and the transmission. Much of it will be caught by the oil filter -- change both the filter, and the oil, but do NOT add more
SeaFoam (isn't necessary, one treatment will last many, many thousands of miles, with regular oil/filter changes). YMMV. Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII