What's the attraction of the AV without sheaim, anyway? I don't like rampaging demons and plagues and plummeting property values.
Sacrifice the weak is a big one.
Some civilizations are also less effected by the armageddon counter than others, so can gain competetive benefits by hurting everyone else more than they hurt themselves.
The Elohim ritual also might help somewhat, as it allows them to slow the rise of the counter somewhat. (Though I haven't actually tried this.)