It is hard to imagine toilet paper jamming a gate valve open. Toilet paper has very little strength when soaked. The "sliding gates" in these valves are quite sharp on the moving end. Kinda like an real thin axe blade. A popcorn kernel from the kitchen sink could jam a valve open if a guy is really unlucky. Or the grand daughter flushing a rubber ducky down the toliet. Cute!
If something is jammed in the drain valve, it probably feels like it won't close all the way. Does your valve appear stuck open when trying to push it shut. Debris in the valve would cause a significant leak. So when your tank is half full of water, valve shut, do you see a significant flow out your sewer drain connection? More flow than a slow drip.
The cause of my leaking valve was a cut seal. Mine was just a slow drip leak, but after 400 miles on the road, I got maybe a cup of water when I took the sewer connection cap off. I agree with trying to pressure spray the valve area through the drain manifold. If repeated spraying does not get it, I am afraid you will have to disassemble the valve and examine the seals. At least the parts are cheap!