Another "fringe period" are the Seminole Wars. This reenacting area really covers two periods, the First and Second Seminole Wars. The First Seminole War is an offshoot of the War of 1812 period, and shares the same style of uniform and clothing. The Second Seminole War is pretty much a style period all to its own, starting 10 years prior to the Mexican War.
The reenactors who do the Seminole Wars are almost exclusive to Florida, but they do a respectable living history program. For right now, there are a small handful of sites that are devoted to these reenactors, but they are certainly worth checking out. Florida Military Historians is an overview of the period and a portal site to the other sites that deal directly with the reenacting groups. There are also links here to individual reenacting groups for the period. The other two sites are Yahoo! Group sites and require moderator permission for complete access. The Southeastern Culture group covers the native American side of the Seminole War equation, while SemWar is geared toward the US side of the conflict.