You'll note I said "was designed", not "is currently", so we already agree on that point. I was talking about WED's intentions in 1970 and trying to more perfectly achieve them.
The Haunted Mansion
is in New England, actually. That's a blog post but it has real sources. I'd recommend Passport to Dreams anyways, it's great. The original design for the WDW HM, as the above link shows, was actually more in tune with the Colonial style. They ended up capitulating to the more visually interesting choice. That kinda already ruined the whole thing.
The Riverboat is based on the Mississippi River, yes, with reference to Mark Twain specifically. He and Walt were both raised in Missouri, which was probably part of the reason Walt incorporated his fiction into DL. Basically I'd say the RoA and TSI are both meant to represent Missouri but fit pretty cleanly into the 19th century. Missouri also lies literally in the cradle of a loop from New England to Texas. It's a clever bit of design.
As for whatever genius decided that the Diamond Horseshoe is in Liberty Square, I'm stumped. It almost seems like a mistake to me, considering it's so obviously a 19th-century Old West Saloon.
CBJ probably owes more to Bakersfield, California than the South. To my mind Country-Western music counts as a Western attraction, even if it's an anachronism.
Basically the bones are there but over and over they gradually loosened the rules to fit attractions. It started with the time period for the Mansion facade, then the time period for the Country Bears. After that Splash ended up being in the wrong time period AND location but at that point who really cared?
My point is that they now have a chance for Frontierand to be a proper Western land, if they so chose it to be.