I concur and echo Mullaney .. I have carried a form of heavy CDL from 1978 and beyond the inception of the "federal" CDL in the 1980's , with hazmat and tank endorsements...
1: Generally nowadays, when diesel is transported in bulk (more than 119 gallons), it is regulated under the HMR and requires placards, and it also may or may not require a hazmat endorsement and CDL...
2: A sticky keyword in the regs is "Commerce." The definition of this per DOT and its interpretation by enforcement agents in every state affects many aspects of many things. You can start with :
federal-hazardous-materials-transportation-law-overview but don't stop there .. THERE IS MUCH MORE TO RESEARCH at other agencies
3: Your subject matter can be a complicated one and there are many contributing factors to reach a final determination as to your individual situation . Frankly, you would likely be better off to not use the trailer and instead make the tank a permanent part of your truck as a vehicle fuel tank in order to meet the exceptions to the HMR.
4: You have a lot of studying to do, and perhaps it would be wise to get an official in-writing determination by the pertinent agency, something you can carry with you to educate any "errant" DOT agent or LEO you may run across
5: And as far as slosh goes, when I left active duty I began hauling milk, those tanks are not baffled for sanitary reasons... I remember one time getting quite a jolt, although I was expecting it, when a car passed my trac/trailer just before a stop light and blocked my lane .. Since I was still in the middle of my pickups for the day, the tanker was about half full.. I was able to get the truck stopped barely in time but when the 2nd slosh returned to the front bulkhead, I wasn't holding the brake pedal with enough force. The truck got pushed forward about 3 feet and almost rear-ended the donkey in front of me. (woulda served him right)