We did the east-west trip May - August.

After a lot of discussion, the only real discriminator on which way to go that I find convincing is staying out of the sun's glare. I'm more concerned with a driver who can't see me, coming up behind me, so he can move into the other lane, than I am about the driver who'd have to come all the way across the road to hit me. Based on that, I'd say ride east if you'll start well after dawn, and perhaps ride into dusk; ride west if you'll get up and ride early, and be off the road well before dusk.

As it turns out, we did the early ride -- too many 90-100 degree days in Kansas for me to ride late in the day.