Sounds like the previous owner(s) didn't take very good care of their black tank. Yes, sensors can be troublesome but also can be fairly accurate if the tank is subjected to a procedure that will prohibit build up on the sensors.
I have found the best way to accomplish this is to empty the tank and flush out prior to traveling. I put about 5 gallons of water in the tank along with a cup of liquid laundry detergent (I use Oxy-Clean) and a 1/2 cup of Calgon water softener. While traveling to my next destination, the solution will slosh around in the tank "loosening" any residue left in there. Upon arrival at my destination, I'll drain the tank once more and put another 5 gallons back into prior to using the toilet.
This procedure has worked for me will all my rv's from our first single axle trailer to our 44' motor home and I highly recommend it.
In the OPs case, this procedure might take two or three trips to eventually get everything off of the season.....but it will work.:C
Hope this helps
Ron