My local market supplies pasture raised beef shank at 2.29/lb and chuck eye roast for about 3.29/lb. Oxtail from the same pasture fed farm is slightly more expensive at around 4/lb and they're trying to order me some liver for under 4/lb. While yes it is an amazing small chain supermarket that is only up in my area you might be able to make do with the occasional pasture fed meats if you go for the odd and underutilized cuts that I mentioned above. Additionally meat marked as "stew cuts" is normally from around the shank as well as it a great price since most people don't buy it (supply and demand).
Tongue and heart is also often pretty low for the same reason but can end up very tasty. As with the shank/roast/stew/oxtail cuts you're going to want a nice long braise with the tongue as well, these muscles are worked almost nonstop over the entire course of the cow's life which means they are very tough, but a good 3-4 hr braise (make a lot at a time for left overs) will make them more tender than a filet! Alternatively if you happen to have access to a vacuum food packer you can try some sous vide cooking (simmer in bag) with some light marinade added in and cooked real low over night 12+ hours, although that's a little out of the general cooking comfort level of most people.
Try checking with your local butchers or even health food stores, while the health food stores will have plenty of the ribeyes an filet cuts for ridiculously high prices, many of them can order you the cuts mentioned above for much more reasonable prices.