Baby Sheep Say Charmin Is Best
I read somewhere recently that according to consumer report that Charmin, and Angel Soft toilet paper disintegrate quickly.
It might be worth a try of either of these, before you bothered to disassemble anything.
It is possible that if paper is blocking the knife (guillotine) valve that when one pushes the valve even partially closed that, that movement is enough to cut and dislodge the blockage.
You could drain and thoroughly flush your tank, then to make a test refill the tank,(with clean water only) and drain it as though it were black water. If it acts the same as with real black water you can then check for a venting problem.
If the water drains uninterrupted and in a fashion acceptable to you, then look at the tissue issue, or perhaps something more substantial as the culprit.
I don't think it is the valve itself per se. If the valve moves freely and seals whatever it is controlling then it should be OK. If there were a material lodged in the valve permanently, then it would (never) function properly.