Instead of SLC, how about a little further south near Provo. Several interesting trips to take from there. Check out my links for those drives
here. Plus there's Timpanogos Cave National Monument to explore up American Fork Canyon.
From SLC, take I-15 to US 20 to West Yellowstone and go into the park from there.
I don't know why you're worried about the performance of your vehicle. You have a lot more HP and Torque than we do and we tow a trailer that isn't much different in weight than yours over many steep passes here in the west. Remember that once you're off the interstates, the speed limits often are much less, so you're not needing to keep up a high speed anyway.
