These three cross-country routes are west to east, which is believed to take advantage of predominant westerly winds. Spring routes on the other hand often start in the American Southeast and head west in order to avoid the worst of the summer heat.
A more Northerly route is popular in the summer to avoid some desert heat, but I can say by experience that the barren plateaus in Montana can exceed 100 degrees during the heat of the day. However you do this, take lots of water.
The Big Ride Across America is a fund-raising bicycle ride from Seattle to Washington D.C. that I joined in 2000. We rode 3000 miles in 48 days averaging more than 83 miles per day after raising a minimum of $6,000 for the vital programs and research of the American Lung Association