It's true that SotS technically takes place in Georgia, but there's nothing about Splash Mountain that's explicitly southern. Just from looking at it/riding it, you wouldn't conclude that it's decidedly not western.
With PatF, on the other hand, the location is integral to the theme of the movie, and given the emphasis on Mardi Gras, it sounds like they'll be leaning heavily into that for the ride as well. Therefore, I think the fit in Frontierland will be considerably worse than before.
But I still don't think it would be the end of the world if they decided that NOLA was "west enough" and just left it as part of Fronteirland. From the outside, it the mountain will always look more western than it does New Orleans.