I emailed a friend who is a Sargent in the Arkansas State Police. He forwarded it to a Major apparently. This is the response based on the M934 data plate.
"From the information (photos) you sent me of the builders plate of 29,280 lbs of axle weight you will need a Class B CDL License to operate it. If you tow any trailer over 10,000 labs GVWR you will need a Class A CDL license. The Class B would require you to take the General Knowledge and the Air Brake knowledge tests and a skill tests to operate the truck. "
Based on what I explained in the email about the driveline brake system as well as the air system on the trucks. His response:
"It is the same three maneuvers that is required for a Class A Semi with air brakes. There will be a restriction on your CDL “E” which means if you take a skill test in a CMV with an automatic transmission you will be restricted to driving only vehicles with automatic transmissions. ( No manual transmission CMV’s). Without seeing how the truck air brake system is set up I would recommend using a standard transmissioned class B truck with air brakes."
All I can say is take it down there for the skills test and see what happens. Or go to a equipment rental place and rent a dump truck and trailer for a few hours. For leaving your M934 there for them to take a look at might get some $ knocked off the cost.