A 10k trailer is stated, we don't know if that is gvwr or loaded weight. A cat scale trip would appear to be in order to determine the actual,.loaded ready to travel weight.
Regardless, if we use 10k as actual loaded weight and 15 percent for younger weight which detracts from available payload, even with just the driver and no other occupants or stuff in the truck cab or bed, the OP will likely be over payload rating on a half ton truck.
Let alone the 35s or the lift, both not good for towing heavy.
He's on the cusp of 2500 Cummins territory with that load going that distance in my opinion. But that's just me, personally. I prefer to have more margin than most.
Stock tires would help as do the already good 3.92 gears, but he's going to be over payload. What he needs to confirm is he will not be over GRAWR with the considered load, especially on a trip that far.
Some folks elect to disregard the weight ratings and wind up ok. That's their choice, I just do not, again personally and would not suggest doing so. It's one of the many reasons I have a 2500 series trick and now 7yrs later, still love it just as much as I did on delivery day.
To each their own.
Happy new year gents!