How about Dungeon Village? It's one of those Kairosoft games like Game Dev story, but it revolves around a little village you develop that sends out adventurers to fight monsters and go on quests. It may be more hands-off than you're looking for, but it matches your desire for hands-off fun watching little guys do little fights.
+1 on Dungeon Village, although it probably doesn't meet the combat style you're looking for. It's a hell of a lot of fun, and this is coming from someone who actively dislikes all of the other Kairosoft games.