At the end of the day, there's pretty much a set group of players willing to play tanks and healers as their mains (ie, "past the leveling phase"), and not a whole lot of incentives will change that, nor get them to group with randoms over a group of buddies (pretty much all the tank mains I know have their pick of the litter when it comes to grabbing skilled DPS from the FC for roulettes).

I think Zojha's solutions are the most elaborate to construct, but also the most effective. Make FATEs easier, more fun, not huge HP sponges if more than two people are clearing them etc. Introduce more hunt logs, or challenge log entries, to help DPS get extra exp. Fix PotD so it doesn't actually require tanking or healing to make serious progress. And maybe up the dungeon format to 1/1/3, or even 1/1/4, so that every healer and tank WILLING to queue for duties inherently has their value spread across more of the DPS pool.