Dave,
According to my new 2nd ed. copy of the late Frank Seller's "American Gunsmiths" there was a Martin Beeman the working as a gunsmith in Lancaster, Fairfield County, Ohio about 1831. His source is listed as Gluckman & Satterlee's "American Gunmakers". I also found a reference to Martin Beeman in my copy of Donald Hutlar's "Ohio Gunsmiths & Allied Tradesman", Vol. I, p. 208. In this book there is a photo of a fullstock percussion rifle by "Martin Beeman". Unfortunately, I don't see much resemblance between the rifle pictured in the book and what's left of yours.
Also referenced is a photograph of a fullstock flintlock rifle signed "M. Beeman" in the Association of Ohio Longrifle Collectors Newsletter, Vol. III, No. 1 (1981). I don't have a copy of this newsletter. Maybe someone else does. The AOLRC used to have copies of old newsletters available on their website. It looks like they're reworking their site and these old newsletters are currently no longer available online.
Good luck,
Mark