To the topic of the thread: BRD/BLM will result in the fastest pulls. Lesser geared tanks who are trying to do the dungeon in 5 pulls will desire BRD/BLM for this reason as they will run out of CDs during pulls otherwise. When I run WP with a DRG/SMN who I am helping gear up, I still have decent success (~15 minute runs). If the tank's gear isn't top tier, just turn the dungeon into 6 or 7 pulls as opposed to 5. It is significantly easier and only adds 3 or so extra minutes.
Just tell your tanks to break apart the pulls a little bit and everyone will be happy.