Maybe designate one team's goal as actively preventing other teams from gaining treasure, rather than to capture treasure for themselves. Or as a "hit squad" out to assassinate a specific wizard, apprentice, or captain.
Over-RPing could be as much a problem as under-RPing, in that you might become so focussed on keeping your guys alive so they can level through a campaign that you avoid all conflict. This is absolutely sensible IRL, but not so much on the level of an individual game. Going to one-off games or nerfing the consequences of failure in campaign play might allow or encourage a more "penny wise, pound foolish" approach, where more treasure is prioritized over characters' lives.
Restrict mobility with terrain more. I'm constantly seeing FG setups here and elsewhere where the terrain is placed loosely, so that players can go directly anywhere in a pachinko ball sort of way. You don't want terrain to be a sieve in this game, you want a roofless dungeon. When minis can go anywhere more or less directly, playing for avoidance becomes so easy that it feels like you have to go out of your way to create conflict for no real in-game reason. Bunch your terrain up to create corridors and alleyways and plaza intersections and the like. Stop making everything so open. Denied the ability to move so freely, the teams can have a higher chance of being forced to cross paths.