It sounds like it is a texture thing mostly?
How about a big roast. Round roast or chuck roast? I can usually get grass fed chuck roast for <$5 /lb. And there is very very little waste with a good roast so every ounce counts as food. I like mine as a rare roast but I understand that pink meat is sometimes hard for the former vegetarians. (or as my friend puts it "I like the taste of rare steak but I have to eat it in the dark")
Or how about stew meat? That is usually REALLY cheap. Make a good hearty veggie laden beef mushroom stew.
How are you trying to make it? We use several meals a week with ground beef as the kiddos like it. Tacos (for me a taco salad) and meat spaghetti sauce (for me ...pour it hot over a plate piled high with baby spinach and stir until the spinach wilts...sometimes I nuke it a tiny bit more if i want a bit wiltier. ) Hamburgers of course....and while I like a rare steak, I do cook my burgers more.
MTA: because it is rare I dont have more to say
"When I got too tired to run anymore I just pretended I wasnt tired and kept running anyway" - my daughter Age 7