I think I'd prefer hand quilting, and that seems more authentic because, even though plenty of people were doing machine quilting in the mid-1940's, this was pieced by hand, so probably would have been finished that way, too.
I always wonder if part of the problem with finishing it might have been that they would then have to decide whose quilt it was and maybe do a second one for the other friend. Or maybe it would have been too much of a reminder of that sad time.
I definitely do not have the skills to hand quilt it myself. I may check to see if there is anyone in my quilt guild who would offer to do it for a price. Then I'd have to see what my DH might think of that.
Thanks for all the input!