Return trip is a bit longer, 345 miles @ nearly 7 hours. Could cut a little bit off (50 miles) by staying in Lolo Hot Springs instead of Missoula. Just an idea on a couple of days.
My brother, Dan, & I share driving a tank of gas or so at a time and cat-nap while the other is driving.
We can cover a lot of miles in a couple days of this before using a motel and then doing it again.