Being a 5ver, this may not be an option. When you flush, can you look down the hole (flash light??), and see into the black tank?
I am suspecting your not using enough water. After dumping the tank do you add about 10% clear water back into the tank. So if you have a 50 gallon tank, do you put at least 5 gallons of water back into it before using the tank again? When you flush are you filling the bowl before flushing?
If there is not enough water in the tank you are creating what sounds to me the dreaded poop pyramid. When the tank is "dry" all the solids land in a single spot and does not disperse throughout the tank.
How to get rid of it! Lots of thoughts. Some people like to dump a few bags of ice down the toilet before going on a drive. The thought the ice will slosh around and help breakup the pyramid. I like using something like liquid fabric softener, others use water softener. Both products changes the surface tension of the water, so it will soak into the pyramid, and helps soften the drying pile. I add about a 1 cup of fabric softener to 5 gallons of water. After dumping (and using the flush), pour more into the tank. Go for a drive, let it sit, go to your next campout, use the tank, fill the tank, drain the tank, flush the tank and repeat. It may take a few applications, as it needs to soak, and needs time to do its job. If you can get a manual wand down the toilet, use it too.
Being a 5ver, I suspect it would be very hard to use a manual tank flush wand.
Before cutting into your walls and vent, I would buy a cheap endoscope that can be connected to a PC or phone, and run it down the toilet or up the sewer drain and see what is going on. https://www.amazon.com/Wireless-Endo...xpY2s9dHJ1ZQ==