Toliet plugged on our retreat

You're saying if you stick a running hose down the toilet with the dump valve open nothing comes out? If you can see TP down the pipe, it may also be clogging the valve. You could try backflushing from the sewer outlet side but that would be temporary. It might dislodge the TP but since you have so much in the tank another wad would probably get stuck again.

If it was me, I'd fill the black tank as full as possible with water, open the dump valve and wait for the TP to break down. The weight of the water will eventually push it through. A clear sewer connection would be very helpful during this process.