I do a lot of backpacking — and a lot of looking at maps/guidebooks when I’m not backpacking — in western Montana (near Missoula), but that might be a bit out of your driving range.
I’m guessing the Beartooths are probably already on your radar? If not, that would be a place to look into and you should be able to find exactly what you’re looking for. I’ve never backpacked there myself but have heard great things and there are some in-depth guidebooks out there that have plenty of trips described in them.
In the areas I’m most experienced with (Selway-Bitterroot Wilderness; Anaconda-Pintler Wilderness; Beaverhead Mountain Range) there unfortunately aren’t a lot of loops. A lot of the trails meander up one canyon to the high country and either connect with an adjacent canyon or are out-and-backs unless you want to engage in cross-country travel. If you can arrange a shuttle, there are some great trips in the 50-70 mile range that would be pretty incredible, although you might end up running into some sketchy trail conditions and/or burned areas. Because of that I typically plan lower mileage days in this area than I do for national parks.
If I had to make only one recommendation, I’d say a section hike of the CDT in the Beaverhead Mountains, west of Jackson Hot Springs, MT, would be a great use of a week in southwest Montana. Only issue is the bugs can be pretty vicious in that area in early August. They’re barely tolerable by mid-August in most years and pretty much nonexistent by the end of August. Depending on where you start it might be a little less than your mileage goal, but I guarantee you that if you make the side trips to the numerous high lakes off the CDT it will be a memorable trip, especially if you fish : )
Feel free to send me a PM and I can share some more of the logistical details with you and the shuttle options for that area.
Happy hiking!