On the D9P I use the same center fabric in all the blocks - gives it some unity
Remember that not only is the center block being cut (in quarters) all 4 squares that touch it are halved.
That said, I would not waste Civil War fabric on a D9P.
Why not make a quilt more typical of the era - even though it wasn't your war.
You could google "Civil War quilt patterns" to get some ideas.
Have fun
and, Happy New Year.