Not to get personal, John, but when would you have been reading this book when you were younger? Based on the type of illustrations that grabbed your attention, my first guess would be 1950s or perhaps 1960s as kids books have become progressively more "in color" over the years and the 1960s, being the centennial, certainly produced a lot of Civil War books for all ages. Basically, I'm trying to narrow down the search by knowing the book can't be younger than X.
On the other hand, it sounds like this could be a family "antique" that might have belonged to a parent or even grandparent. Do you remember any details about that? Who did it belong to? When might they have received it? For example, if my Dad had had a favorite new book from about age 10, that would tell me to look for books from the 1930s to possibly early 1940s, at least as a place to start. With multiple editions/reprints (Grosset and Dunlap, that means you!), the copyright could be even earlier.
The other problem is that period illustrations from Harper's or Leslie's which look like what you provided are still used in kids books even today. It's hard to know if what you saw and liked were those or original artwork in the style of those old prints. Original artwork could lead to an illustrator which could lead to the book.
I'm happy to play with the search, but at this point I don't honestly have a lot of hope of finding your book without more information.