FWIW, the Big Hole (Dillon to Wisdom to Sula) felt like the most remote part of the TransAm I remember. Scenery is very nice (if you don't have smoke when you go through there) as well. To be honest, I don't know what I missed through Idaho and Oregon on the original TransAm, as I went north to Glacier and then took the Northern Tier to the coast. Glacier was worth the detour IMHO!
Speaking of which, the NT is a great way to go west. Five passes in four days on WA Rte. 20, and all of them felt different. Tough, yeah, but after you've ridden all the way from Virginia, it shouldn't be a big deal.
For LouisB specifically, you might not care about the Virginia tidewater and piedmont regions if you're not interested in American history and if you're in pretty good shape when you arrive. Have you considered riding the W&OD rail trail/bike route out of Washington, then make your way to Front Royal, and take the Skyline Drive (Shenandoah N.P.) to the Blue Ridge Parkway above Waynesboro to pick up the TransAm there?
As I said above -
I've had the misfortune of riding and hiking Glacier a dozen or more times.
You said that, and I can't quite figure out if "misfortune" is a sardonic introduction or whether you really don't like it but keep going back.