First, don't rely on the tank readings. They are notoriously bad and just about always indicate inaccurate levels.
Turn off the water supply and look down into the black tank to see how much "solid stuff" is in there. If it's been well flushed after each dump, you should be able to see the black bottom of the tank as it left the factory.
If you don't have a built-in tank flusher, a clear elbow with back flush attachment like the Valterra one may work. There's also a wand you can stick down into the tank. With the water on, you can stand at the toilet and open the valve to let water into the tank. Try and put as much water in as you can so you get a good rush of water to help flush stuff out. May take 5+ minutes depending on how full the tank is.
If still not much success, the next line of attack is chemicals. There are RV black tank treatments available to help break up the solids and crud. Failing that, liquid drano will work as long as you use the type that does not attack metal and you don't flush it into an on-site septic disposal system (extremely important). Our owner's manual says to use liquid drano.
Once you finally get the tank cleaned, it is recommended that you put 4-5 gallons of water in the tank after each dump and flush and use at the campground. When you use the toilet, don't skimp on water when flushing, thinking that you are extending the time before the next dump. Insufficient water is asking for a plugged up tank.
Finally, you *could* buy a "Tornado" tank rinser however you need access to the tank and since you have an enclosed underbelly, it would not be an easy task.
Tornado rinser You *could* also install Horst Miracle probes which are a lot more reliable than the standard button OEM ones, however, there's the same issue of access to the tanks.
Horst Miracle probes There are various chemical treatments you can put in the tank before each use of the tank. Some say they don't work that well and some swear by them. I think "Happy Camper" is one recommended by many. We've tried the ice trick without success. The "Geo method" reportedly works well (just google it).
Remember, lots of water is the key to prevention of this common problem. ;)