Have you thought about mixing the ground beef with ground turkey?
We purchase a 12oz chub of frozen ground turkey for about $1.50 and can get fresh ground on mark down for about $2 per pound. I mix it with the beef and no one has noticed! I usually mix a total of about 10pounds at a time and portion up into one pound baggies.
Good Luck with the beans and let us know what you try please!! Beans would be even cheaper and more nutritious!!