I had the same problem with Black tank valve. Paid $100 for a dealer to check it once, and no improvement. So, I decided to do check and fix the problem myself after reading some great info on this forum back around June.
First, the job is not that hard (but easier if not 6'3"/240 lbs
).
After dropping the belly and removing the black tank valve I found the gasket was deformed and forced into the groove keeping the valve from closing all the way. I replaced the gaskets and lubricated them and the actual valve and grooved track it moves in with plumbers grease; then reassembled. Works great; very easy and smooth. Been working great for the 2 weeks since I fixed it. Now, it makes my grey valve feels difficult, so I plan to repeat on this one.
Like you, I thought it was the cable and maybe toilet paper causing the very stiff valve operation and failure to seal. That was not the case - deformed gasket replacement and valve lubrication fixed the problem.
Here is the link to the Topic:
http://www.montanaowners.com/forums/...ad.php?t=66825
Do take Tank emptying/rinsing precautions before removing the valve
Good Luck!