I've been trying to work out a Polk-led America for a while, and I think you're onto something here. What would you think about:
America - James K. Polk
UA: Sea to Shining Sea: Civilian units receive +1 movement. Gain culture from capturing or settling cities (based on distance) and immediately enter a 5-turn Golden Age when a city is captured (can be extended with more captures).
UU: Flying Artillery: Replaces Cannon. 4 movement. Slightly weaker (18 or 19 vs 20), but may withdraw from combat.
UB: Supply Depot: Replaces Caravansary. In addition to Caravansary benefits, cities with a Supply Depot gain 5%-10% bonus to food and grants an additional Trade Route.
I went with Sea to Shining Sea as the UA name because that's what Polk accomplished, and it keeps Washington from really having to be changed.
Loved the Horse Artillery, which the Americans called Flying Artillery during the war. I wanted to further emphasize their mobility in combat. Having it replace the Cannon would be more accurate, since the Cannon is meant to represent artillery until the Industrial era and the Gatling Gun didn't come into its own until after the Civil War.
The UB is based (loosely) on the Oregon Trail and others like it that settlers used to move west. Giving it the food bonus represents the towns that grew up from the trading posts and forts that lined the trails.
I'm still sad that there's no real way to represent the Prairie Schooner outside unique, easter egg-style graphics for the Caravan, but that's okay.