I too would recommend Option no. 2. Wyoming up to Sheridan can be a bit tedious, but after that the route is pretty entertaining. Don't miss the Little Bighorn battlefield site east of Billings.

I'd probably overnight in Sheridan and either Butte or Missoula, which would break it up into three 7- to 8-hour days. Sheridan is a fun little town, a bit touristy (Buffalo Bill and all that) but with a decent selection of lodging and food.

The next evening I would definitely plan on stopping at the Land of Magic for a steak dinner in Logan, a wide spot between Bozeman and Butte. Best roadfood steak I've ever had, commemorated in a trip report here. It makes it worth choosing this route all by itself.