From East Glacier you might want to consider driving north to just before Babb and take route 464 to get to Browning. We used 89 between Browning and East Glacier both directions with our 24ft Class C, no toad, but you might be more comfortable avoiding the curves and short grades on that section of 89 with your longer length.
I would suggest that upon leaving St. Mary, go north on 89 toward Babb and turn right on Duck Lake Rd(464) to Browning. It is a lot better drive than taking 89 to Browning.
We followed this advice last summer and it was a good option. Still quite scenic.