That's great! It's so wonderful to have letters like this.
I'd do what you suggest: scan them and upload them as photos. Not only does that get the whole letter shared without you having to transcribe it, it enables others to see the handwriting and get a "feel" for it.
I'd also transcribe bits. You could quote from the letters in the person's bio or in other bios where appropriate. You can use the personal memories sections for this.
Regarding the civil war service, do you know the unit? There might be some neat things you can do with free-space profiles and/or categories.
If all the letters are around a theme, you might do a free-space profile for "The letters of Warren Lathrop" or whatever.