I am not sure if this helps at all. The following research does place George W. Clement in NH and MA during the Civil War era, so you might still search there.
I find who seems to be your George W. Clement, son of Christopher, b. in Plaistow NH being married twice.
February 10, 1859 MARRIAGE in Springfield MA: George W. Clement, residing Manchester NH, age 23, Teacher, b. Plaistow NH father Christopher Clement, etc.
married to Linda A Washburn of Springfield age 23 b. New Salem , dau of Obed Washburn, 1st marriage for both
George W. Clement, son of Christopher & Ann, married 5 Dec 1862 at Springfield MA to Julia H. Brewer, dau of William E. & Eliza T. of Wilbraham. [NOTE: In this marriage record he lists himself as being "OF Willoughby Ohio", age 26
I looked in the book, Manchester men. Soldiers and Sailors in the civil war 1861-66 and did NOT find his name there.http://archive.org/details/manchestermensol00gilm
Best wishes with your research.