I just do the scumbag move and scam the dungeon finder tool. If I'm playing a hybrid class I just set my role to a tank or healer and fish for another tank/healer, then I'll change my role when they join. On my Hunter alt I just invited a hybrid DPS class and explained it to them and change their role, lucky he's 863 now so I don't have issues getting invites.
Yes, I know it's a dirty trick and it's probably frowned upon by many, but it's kind of a requirement if you don't want to wait for a while.
Also another thing you can do when your item level is high enough is just demand a stupidly high ilvl to join. So on my Hunter I just set it to 860 required and it seems to find a good amount of tank/healers as I guess they're all after groups with high item level.