The battlefields do make that tricky. They're not about quests and story. They're about emptying dungeon levels of monsters. Anything other than Hack & Slash is out of place there.
Well, then we'll set up the battlefields to award experience per kill and have each new level, and each time you leave the battlefield, as a checkpoint.
Or they could redesign them so that the battlefields aren't just combat. What if one dungeon was combat, one was booby trapped and lever puzzled beyond belief, and the third was... I dunno... something magical like.