David, needless to say your photo did not post. It seems that technology is growing at a rapid pace and I am just giving you a road that may want to explore. Have you considered using facial recognition? They do have facial recognition software available now with digital photographs. In my view a facial recognition expert's opinion may have a desired affect. Your particular issue is somewhat unique since you appear to have two photographs of what could be the same soldier within a short timespan. A facial recognition company or service could use their technology without compromising legal issues since the soldier's photographs are 150 years old. It could be good advertisement for the company or service providing this relatively new technology.

I still believe however the old method of doing genealogy may also be beneficial to your scenario. Sometimes doing genealogy can take months or even years to find.