I didn't notice any markings on the monument indicating when it was installed or who installed it, so I've spent the past week doing Internet research and contacting the Rockingham County historical society looking for more information. My search has proved to be fruitless so far, but I went ahead and submitted the waymark for approval. The approver guessed that the date of the monument was between 1900 and 1925, based on the style, so I chose 1915 as a guess until someone can provide better information.
It was a nice visit, and I enjoyed reading the inscriptions on the monument. It was near sunset when I stumbled on the monument, so all of the pictures I took have that "end of the day" quality in their lighting. I like how they turned out, especially the one I used in the waymark page and the one that's included in this post. For the one included in this post, I even got to spend some time with Photoshop Elements to remove the power line out of the background of the picture (before and after), which I think turned out pretty well.
I'm continuing to have a good time learning more about the US Civil War, both through "book learning" and through visiting historic sites and monuments related to the war.