What I think is that the rear carb is flooding out. The float is too high, could be trash in the seat, float sticking and not shutting fuel off.
Also check the vaccuum hose to the petcock. Cracks in the hose can keep the petcock not work right, not allowing enough fuel to the carbs.
Hope this helps you.
I think niterider is on the right track, when the rear cylinder is so wet and black, and the front cylinder is clean and burning right. Something is not right in the rear carb, or some of the old foam filter is sucked in there as Cindy surmises.
Cindy, just a note regarding the spark plugs, just because they are new, doesn`t mean they are any good. I think I read a post here just recently from somebody who installed new Champion (?) plugs on his bike and it ran like crap. Put on some new NGK plugs, which are recommended for this bike, (and I don`t recall if they were Iridiums or not), and it ran like a champ.
Likewise my next door neighbor, who was an experienced auto mechanic, installed some new Motomaster plugs (a cheap Canadian Tire Co. house brand ) in his 850 Suzuki one weekend, and the bike would hardly run. He swapped them out the next weekend after 4 round trips to Calgary, and about 1,000 miles on the plugs. He put in a name brand, maybe Champions, and it ran like a new bike. Some engines, or makes of engines, just seem not to run right with some brands of plugs, whether they are the suggested replacement part or not. I do not know why, I just know that in my experience, it is true.
I hope you find and cure the problem without too much more grief. This is the time to be ridin`, not wrenchin`.