Definitely tie it and maybe use a dark tan or brown thread/perle floss for even more authenticity.
A cotton batting such as the Quilters Dream Deluxe loft would be slightly thicker than we normally use and would more closely replicate a heavier utilitarian quilt of the period. Your dad will just love this!
By the way, has he been back to Appomattox in the past 10 years? It's really looking so nice, and the town has just received a new museum about the War.
Jan in VA