Both the Chi to Seattle route (westbound) and the Sea to Chi (eastbound) are excellent, and in May you will have incredibly long days so less of the trip will be lost to darkness, but if I had to choose one I would pick the westbound route. You get to see the Dells in the early evening light, sleep through the slightly monotonous parts of western MN and eastern ND, and then you get to see the northern plains roll by all day on your second day. May is a good month to see them because the range is usually pretty green and the wildlife is pretty aggressively feeding so you see a decent amount of deer and antelope, though most in the early morning or late afternoon. And then in the late afternoon you begin to see the hints of the Rockies to the West and as the sun sets behind them somewhere around West Glacier it is a beautiful sight indeed. Then you wake up in central Washington and it is verdant and a great countryside to watch out the window.
You get most of Glacier in the daylight regardless of which direction you go, so you can't go wrong.
In May sunrise up on the High-Line is around 5:30 and sunset around 9:00 pm, so the days are long and usually very sunny.