This problem should be one known to occur even prior to becoming a DPS. iLVL90 Dragoon speaking I always found it easier to have FC members run raids/dungeons with me considering if you're a growing company you should have new players working through the ranks so you can run different dungeons throughout the day or whatever.

Doing ''shouts'' on what dungeon you'd like to run and even making a PF yourself could probably cut down the time. In all you'll wait it's every DPS nightmare and it will only get tougher with the influx of DPS with the new class getting ready to take off.