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No you will not hurt the engine. Running less that full loads is easy in the running gear. You consider a smaller truck or a car for the grocery getting. Even with small loads your mileage will be considerable less that with a smaller truck or car. I worked in construction when I had...
What did you test? One problem with earlier diesel trucks is a broken "shower head". This is part of the fuel pick-up in the fuel tank. They can break and cause the truck to "run out of fuel" at about 1/4 full. Do you have two fuel tanks? Is this problem with one tank or the other or both...
"unfortunately the lack of chatter also means they are slipping instead of grabbing, which is literally the opposite of what you want." Not entirely true. Think about a clutch. You don't want the clutch to chatter. You want it to be smooth when you disengage it and engage it. The clutch will...
I would remove the current oil and add regular diff oil. Drive it for a little ways (50 miles or so) and change it again. This should get any friction modifiers out. You should be GTG. [Good To Go]