No experience with route 34, but there is a third route I didn't mention in my earlier post.
We have twice used route 89 all the way from Brigham City UT to Grand Teton in our 24ft class C. Between Logan and Garden City on Bear Lake route 89 is the
Logan Canyon Scenic Byway. Heading south, you will have to climb a 6-7% grade for 1-1/2 to 2 miles out of Garden City. The downhill to Logan is gradual, but the road is winding so it isn't always possible to drive the speed limit. It's a very pretty drive that we wouldn't hesitate to do again.