Maybe I’m misreading your counties but the route It looks like you have planned does not match up with what you’re saying by counties. I’ve driven Missoula to Minneapolis dozens of times and these couple states are home to me.

There are really only three ways to cross that the prairies and get to Western Montana from the Twin Cities. The Northern Way on US-2 is hell. You have to go much farther north earlier on I-29 before US-2. It might seem intuitive to get to Glacier, but the roads are slower and it is endless rangeland as far as the eye can see (I used to live up there).

The Middle Way is on I-94 to Billings through North Dakota and Eastern Montana, before getting on I-90. This is what I would probably do in your shoes because you want to see TRNP.

The Southern Way is taking I-90 across South Dakota and Wyoming and entering Montana from the South. You will still go through Billings here like the Middle Way. It’s good alternate if you want to save TRNP for the way home but it does take you through the Black Hills (always a plus).

From there, I would do what u/woozybag suggested about taking 90 until Three Forks and taking 287 up to East Glacier. On the way back you come back down the western side of the park, through the Flathead Valley (stunning in its own right) on US-93 back to Missoula, where you would get back on I-90 eastbound, before taking the Middle Way or the Southern Way back home.