We put TP in our tank - use plenty of water when flushing the toilet ( 2 bowls when TP and solids present) and have lived full-time in our RV for almost 3 years. Never a problem. We do not use any additives other than lots of water.
You don't need the sensor to tell when black needs to be dumped - it will start making a gurgling/burping noise when you flush. You will know that it need to be dumped in a short time. We use any TP that says "septic safe".
I'm sure that the tanks were designed and meant to have solids and TP in it. I would use public facilities before I would put my TP anywhere other than the toilet.