I've made four transcontinental flights using a variety of routes.
Looking at your proposed flight, I see that the northern route through
Yellowstone and SD runs way north of the great circle. If you want to
go to Yellowstone, that is managable, but you will have some higher
terrain to deal with.

I'd suggest flying a bit south of the great circle, passing through
Tucumcari, NM. This will be only a bit longer than the great circle,
and will not require O2 or mountain flying training. (However, a
number of flight schools along this route do offer it, and it would be
a great idea.)

If you want a northern route, I would suggest crossing the Rockies
through southern WY, staying near Route 80. That is another low spot
in the mountains -- you can fly around 9,000 most of the time and you
will not need any O2. However, the weather is less reliable on that
route, so you may have to use the Tucumcari routing both ways.

Paul Hamilton