Here is a link to an example of one of the gravestones.
We've seen this shape elsewhere, too--U.S. route markers, some law enforcement badges. But where did it come from? Why put it on all the Union soldiers' gravestones (and even those of some civilian casualties)? It also appears on the gravestones of civil war veterans who died after the civil war (even decades after), but, as far as I know, not on the gravestones of U.S casualties of other wars, before and after--why? I've done some searching on Google, but I got nothin'. Thanks.
Best guess? They're derived from early U.S.A. Republic iconography. Early U.S. drawings, lithographs, publications, etc. show similar shields. Historically, the shapes of ACTUAL shields and escutcheons derived therefrom are a bewildering variety. Books on Heraldry show hundreds of different designs JUST for the Middle Ages. Throw in ancient, classical, Renaissance, and modern fanciful ones derived from all that I have previously listed, and you get thousands, possibly more than 10,000, unique shapes visually recorded in all of our written history.