A good way to encourage fighting the mobs would be some kind of positive reinforcement. For example, in Dungeons and Dragons Online, players accumulate an XP bonus (10-25%) based on the number of monsters slain before the completion of an instance. The highest reward is only offered for slaying all monsters in a dungeon.

This could apply to XP or SP. I'd imagine something like this would encourage more players to defeat many of the mobs, while the players who just want to rush the boss for the gear drops could still have their cake,

Not really a suggestion (but it could be). Just demonstrating an example of good design. I realize not everybody likes the idea of borrowing concepts from other MMORPGs. This one, however, seems okay to me.