Headwinds or climbing? Climbing is nearly always the least psychologically damaging. Nearly always! Reverse your route. You won't notice the slow elevation gain, but you darn sure will notice headwinds. And they ARE more likely to be S/SW/W.

If you can't figure out how to get your bikes aboard a train/bus, then consider shortening the trip so you'll have plenty of time to explore the parks. Another option is to hire a local with a truck to drive you down the road a ways. You'd be surprised at how easy that can be. Folks like to help people on bicycles, especially a touring couple. A small town 'mom and pop' cafe or bar are good places to inquire. Or even the police department. They know everybody in small towns.