This does not pass the smell test. Well, maybe not smell, but it makes no sense. Back during The Great Depression, mayonnaise would have to have been made by hand. Almost all Southerners had no money to purchase items at a store.
My Southern family, Great-grandparents on down, never ever mentioned putting mayonnaise on a peanut butter sandwich. Back then peanut butter had to be stirred every time it was used so spreadability was not a problem. If they ate eggs, they ate them and didn't take the time to make mayonnaise like some hifalutin restaurant would serve.
Gibs me dem BOILED peasnut and I yam yours for attornity!
Crumbled corn bread in buttermilk for you