Is everyone forgetting the RDF Daily Heroic? It has a reward of 2x Badge of Justice + 13g20s.
Unlike RDF for Normals, RDF for Heroics is like playing Minesweeper, except without any clues. 15 Heroics + tank doesn't matter + shaman (Lust) + mage + lets say you always want more than middle of the pack dps spec so 10 specs out of 20 for 2 dps spots. So, you have 25% chance to not step on a comp bomb for the Daily Heroic.
You can can control for the rest of your heroics by
- having a sense of the ranking of heroics, lets say from easiest to hardest: UB < AC < SP < BoT < Ramp < SV < SH < SL < Mech < BM < BF < SHH < MT < OHF < Arc < MGT (not out yet)
- only using social means: friends, guild, /join Global chat for LFM
- getting addons to help you spot or make groups in chat, e.g. wQueue or GroupBulletinBoard, AutoFlood to repeat posting automatically
- then inspect players for any lingering greens, except possibly jewelry (neck/rings due to Jewelcrafting) and maybe one trinket (from quests). Every gem socket except meta gems needs a gem, but enchants not necessary at all, until maybe the very hardest Heroics (SHH and above)
- oh, and as you can see from the list above, for RDF Daily, maybe bank whichever keys you dont want to have to deal with, e.g. Keeper's of Time key. This will eliminate your ability to queue randomly for them until a week or two when everyone has a bit more gear
- while healers CANNOT carry a heroic (this isn't WotLK, since each mob in TBC heroic can have brutal mechanics and damage), don't enter a heroic without a 227 +Healing weapon and at least one [Lower City Prayerbook] (requires Revered Lower City reputation from Normals + questing).
With all of the above you've given yourself possible chance. Just by using social means alone, your endgame heroic experience will vastly improve.