Buy sustaining potions, and when you're both in combat, just rotate through cooldowns so that you're both dealing damage as much as possible. With Sustaining Potion up and regen on, you should be practically unkillable on PLD, even in the deeper floors, freeing up your WHM friend to DPS.

Also don't hesitate when you go up a floor. Handle any floor debuffs that need to be handled with Serenity, if needed, check for patrols, and then proceed immediately to killing monsters to unlock the passage. You know that you'll have to kill something like 6~10 monsters to open up the teleporter, so hop to asap.

Don't underestimate things like Witching Pomanders or Serenity pomanders if you find extras and haven't opened the rune of passage yet. Turning a monster into a chicken or toad can drastically reduce GCDs spent on healing/sustaining potions used, which will slightly speed you up.

Lastly, once you've learned the monsters a bit on jobs you feel safe on, you could try coming back as duo DPS or 1 DPS, 1 Tank.

Make good use of Sprint. Don't be greedy about chests if you don't need pomanders. S'all I can think of, really.