I took US 2 all the way from the UP to Redmond, WA in 2009, dragging a 5,000 lb trailer with a Jeep Liberty, which was rated to tow no more than 5,000 lbs. It was quite doable then, and should present no problems to you with your rig.
US 2 does have some slopes that grade out in the 6% to 8% range, which is typical of the Interstates as well. I understand your trepidation, but you should be fine, as long as you are aware of the two hazards of such grades: (1) on the ascent, your truck will be working hard, and you would do well to watch your engine temperature, as it will rise above normal; (2) on the descent, you will need to mind your brakes heating up. Both these can be managed by using your gearbox and not attempting to go too fast.
Climbing grades, make use of your lower gears to keep the engine revs up. This will help your water pump move the maximum amount of coolant. On the way down, do the same. This will put as much braking on your engine as possible, to minimize brake use. Going slowly gives the heat build up more time to dissipate, thus keeping things cooler.
Going up and down at 45 mph rather than 55 or 60, using 2nd or 3rd gear rather than 5th, and you can climb or descend 6% to 8% grades all day without issues.
For the most part, US 2 is a fine 2 lane road that passes through some beautiful places in the heartland of America. There are lots of tiny towns and open farm/rangeland along the way.
I also drove 101 from Washington to SoCal on that same trip. Persons who have a fear of heights are advised to drive it northbound rather than southbound because that puts them on the land side of the road rather than looking over the cliffs into the sea. But the views are more spectacular southbound for that very reason.
Honor your spirit of adventure: do the trip, man, do the trip.