When Stephen was on hemo, I cooked an "eye of round" every week so that he always had beef for a sandwich or dinner. It's a good source of iron. It's not that expensive and relatively easy to cook (rub with dijon mustard, or garlic powder or pepper and roast at 450 F for 1 hour; let sit for 20 minutes; works for typical 2-3 pound roast). It's worth a try.
Pelagia ..er whats an 'eye of round' ? never seen or heard of that over here ( plus steak/beef is quite expensive over here)