Going the whole way across the continent? I'd use Boeshield again, but not quite the way the directions call for. Start with a handful of paper napkins (from a diner) and wipe the chain off. Apply the Boeshield, then wipe it down, then let it sit overnight. Reapply weekly, after a couple days of rain, or when the chain starts squeaking.
I might use a dry lube in the dry west (roughly eastern side of the Cascades to central/eastern Kansas). I need to re-apply a dry lube every 4-5 days, or after a day of rain. That's about how long it takes for the chain to start squeaking, IME. There may be a better dry lube than the three or four I've tried. And my daughter can hear a chain squeak about a day before I can, so trust young ears more than old folks' ears!