Although I cannot offer any suggestions regarding your issue(s), I will offer an observation:
Our use of the PC has changed somewhat in that we no longer do the 'hit and run' of a single overnight but now plant ourselves at a location and use the TOAD to explore from it for 3 or more days.
Yes, I agree with the use of both the Sani-Con for "hit-and-run" stops, and the 3" drain hose for longer stays, or when we want to flush out the tanks. Since we're still trying to figure all this out, we're experimenting with various methods of dumping, including not dumping at all for a single night if there is no immediate need.
And more than just experimenting, we're practicing. (Gotta remember to make sure the gray valve is closed before dumping the black!!!
Consequently, I had the factory install the valve on our PC's 3" 'emergency' drain port and found that while the Sani-Con does the job expected, using the 3" 'stinky-slinky' port provides better evacuation of the black tank's solids. I'm sure this is due to the surge of the greater volume and faster flow of the large port versus the slower Sani-Con system.
I learned this the hard way. It is a long way from the end of the 3" dump line to the black dump valve!!!
I found a "twist on dump valve" that just, yes, twists on to the end where the cap sits, then attach the cap to that twist-on valve. So far works like a charm, it is attached very snugly, so far it seems like it won't accidentally detach. The cap, however, is another matter: it was loose, so I wrapped layers of black electrical tape on the prongs, and it is now firmly attached as well.
As for some other means of connecting the Sani-Con nozzle to the campground's sewer connection: laying the nozzle without screwing it in would require some form of weight to hold it in place, such as a concrete block, which we don't want to carry, or a large, heavy rock, which is not available at the park where we're currently staying.
FWIW: I did contact Thetford regarding this, and they have no solution. I'm currently contacting stinky-slinky sources to see if there is some way to adapt their connectors to the Sani-Con hose. If I learn anything useful, I'll add it here.
Thanks for all the feedback, I'll be asking more questions, as there is a bunch of stuff we still don't know. Hopefully there won't be any major damage to the surrounding community in our quest to figure it out.