While I certainly defer to the experts, if you don't mind some "dirt" you could head east from Missoula to Rock Creek Rd. Not sure if there are through frontage roads all the way. We rode I-90 for about 3 miles from the start/end of Rock Creek Rd. to Clinton. Take Rock Creek for about 40 miles and hang a left towards Phillipsburg. From there, take MT 1 to Anaconda. Crackerville Rd. will take you to an I-90 interchange (No. 211), but you can follow frontage roads (Bossard, crossing under I-90 to Wild Horse Meadow and then Nissler, some portions are unpaved) all the way to a trail that takes you into the center of Butte. From Butte you can take Continental Drive to MT 2 over Pipestone Pass (not as hard going west to east) and continue east to Whitehall, which would hook you up with the L&C route. There is camping along Rock Creek, in Phillipsburg, Georgetown Lake, Anaconda and Butte.
Subsequently made this:http://ridewithgps.com/routes/9447008
I have ridden all the roads at least once (some of them twice) in the opposite direction except the miles between 157 and the end. The on-line map does not show a through frontage road between Clinton and Rock Creek, but maybe it's wrong. IIRC, the forst 10 miles of Rock Creek are paved then it turns to dirt until you cross the creek for the second time and make the climb over the ridge to Phillipsburg, where there is a nice motel/campground on W. Broadway just of MT 1. Grocery store across the street and a short walk into the center of town. In Butte the route takes you by the Hotel Finlen. It's a nice place to stay if you want to stop in town for the night. A room in the kitchy motor lodge portion won't break the bank. Get a first floor room and roll your bikes in. There is a KOA in town, but it didn't look nice and it's right next to the interstate on Kaw Ave. As you can see, Pipestone Pass is very gradual. The descent should be fun. I had a head wind both times I climbed it in the opposite direction. The shoulder is somewhat small but the traffic was minimal. Heading east, I suspect it might be busiest in the late afternoon/evening with people leaving Butte.
Let me know if you would like more details.