The only way to make time is on THE BIG ROADS. Last time to Wyoming, we took I-80 to Ogallala, NE, then the state roads, but this year we're going I-90, right around Rapid City/Sturgis. Getting off 90 at Buffalo, Wyoming and running through the Bighorns. We're dropping our trailers In Cooke City, Montana (northeast entrance to Yellowstone)...and riding from there. I-90 is definitely your best bet, being way up there in the northern part of Illinois. If you've never gone I-90 to Sturgis, I'll warn you ahead of time, It's the most boring stretch of road you'll ride. Rolling black ribbon and corn! But once you get to those mountains, you realize the ride was worth it. Good thing you've got an Ultra Classic, you're gonna need that radio! Highway patrol are almost non-existent out there, so set that cruise at 80 and hang on.
It also depends on what part of Idaho you want to go to. We're just gonna make a big loop around it...I've got friends in Spokane, so we're going clear to the top and cross over into Washington.
Have good ride. If you're an AMA member, check your AMA magazine from a few months back, it had a great article on the roads to ride in Idaho. I'll see if I can find mine (I put it somewhere where I wouldn't forget where it was...but, of course...) I'll post the roads they mention here in a couple of days for you.