I have no doubts that your family information that George W. Baynes died duing the war is correct. The question is was he in military service when he died? His service record seems to end with his leave in October of 1861. There are estimated to be maybe 2 million civilians in the south who disappeared during the war or shortly thereafter with no "official" records that cover their passing.
My GG grandfather never came home from the War. His service records ends in Setember of 1863 with no explainations as to why. I surmize that he was killed at the Battle of Chickamauga since his unit was there at that time. His wife disappeared with no record as well as the rest of the family except for my GGrandfather and two of his brothers all of who were living with other families at the wars ending.