I've never been on a timed run through Coutts, but I was through there a couple of years ago.
You don't say which way you're going -north or south - but crossing the border shouldn't be too much of an issue unless you get behind a bunch of motorhomes!
There is a gas station/duty free on the Sweetgrass (US) side - it's just to east of the border crossing. BTW it's the only gas station around, there's nothing in Coutts.
I know there's some Calgary guys that have made the run to Montana recently, but I don't what crossing they used. Perhaps they'll chime in.
Hope this helps.
ian