Imagine back in the day, with 3 at best trans gears, 200hp, maybe 350 lb ft of torque.......we got up and down them mountains......
At elevation, one loses 2-3% of the base HP your motor has if running a non turbo super charged motor. So if in Yellowstone at its highet point of 10,000', you are down some 20-30%. So you WILL go slower. The interstate grades are legally speaking, no more than 6 to a max for short stretches of 8%. Local roads on the other hand, Forest service roads are worst yet. These can get into the 20+% relm. Most new tow ratings only test to 12% max. so potentially, at max gcwr, you could stall out. probably not.....but then again.
I personally would not trade in your truck on a diesel because you will go a bit slower. You will and can get to the higher elevations, ie above 6000' just fine with what you have. Safely and sanely no less. Many have done it before, at or over gcwr. As I was with my 88 K3500 ext cab, about 500 lbs over, and 2500 lbs over with my 96 K3500 with a TD. It outperformed the 454 BB in the 88, pulling the same trailer, 10 years later, kids were not adult in size......Same truck with a vortec 454 would have been under its ratings, same if it would have had an auto, the emanual was deducted 2000 lbs or so.....but I out performed everyone I knew with the POS 4L80E! With that in mind, enjoy the trip!
Marty