I'm afraid to ask what "paleo" is. Some kind of all-meat "caveman" diet?
But the secret to eating meat is to eat it in small portions, used to flavor dishes, not just BE the dish. Make stews and soups and salads and side dishes with meat IN them but not. Also, eat lots of non-prime cuts, which often have more flavor anyways. The best tasting part of a cow isn't the filet mignon, it's the brisket, or the cheek, or the tongue. And leave the bone on, and use the bone. Look how poorer countries eat meat: a small bit of lamb shoulder makes a rogan josh; a pinch of beef cheek becomes a cabeza taco; a small amount of ham or sausage makes a salad come alive; the best posole has just a few grams of chicken in it. Oxtail is really good. Beef bones can be had for almost nothing and are the basis of fantastic soups and stews.
If you're looking for a way to eat almost entirely meat, but you want organic, you're going to have to pay. But even then, concentrate on cheaper cuts. Leave the 2" steaks for richer people, and know that your tripe or pulled pork has ten times the flavor.