You'd probably want to go northbound anyway, based solely on temperature. As summer keeps getting hotter, you'll be farther north. You don't want to be in Texas in July or August, or even late June.

Why ACA suggests doing almost all of their routes westbound and/or southbound, I'll never know (Pacific Coast is the only one that makes sense to do so). More headwind, and hotter areas later in summer. Brilliant, I tell you!
Anyone at ACA reading this: You hiring? Sounds like y'all could use insight from someone that's done some touring.