Can you get bulk cuts and mince them yourself? I often see whole rump for about $8/kg (was actually $6/kg here yesterday) or gravy beef. You could mince these in a food processor after removing the majority of fat and still make meals that go a long way for a family (as opposed to just steak dishes).

Soups would also be a cheap meal with lots of bulky filling stuff like pearl barley or soup mix/risoni/rice/pasta and loads of vege. Very little fat.