I completely reworked the previous implementation.
Now upon defeating Garrosh Hellscream for the first time on Flexible, Normal or Heroic Mode the player will receive a one time quest per difficulty, which will give the player the choice to select one Heirloom fitting for their class, in other words, the list your class sees will have Heirlooms for all 3 loot specializations. As previously, the quest remains to not be account wide, so every character on player's account can complete all 3 quests (Flex, Normal, Heroic Mode Versions).
Here is a table which reflects which Heirlooms can each class choose from:
Class
Heirlooms
Warrior
https://db.pandawow.me/?item=105679
https://db.pandawow.me/?item=105678
https://db.pandawow.me/?item=105680
Paladin
https://db.pandawow.me/?item=105679
https://db.pandawow.me/?item=105674
https://db.pandawow.me/?item=105676
https://db.pandawow.me/?item=105678
https://db.pandawow.me/?item=105680
https://db.pandawow.me/?item=105675
Death Knight
https://db.pandawow.me/?item=105679
https://db.pandawow.me/?item=105678
Hunter
https://db.pandawow.me/?item=105670
Shaman
https://db.pandawow.me/?item=105674
https://db.pandawow.me/?item=105676
https://db.pandawow.me/?item=105677
https://db.pandawow.me/?item=105672
https://db.pandawow.me/?item=105675
Rogue
https://db.pandawow.me/?item=105672
https://db.pandawow.me/?item=105671
Monk
https://db.pandawow.me/?item=105676
https://db.pandawow.me/?item=105673
https://db.pandawow.me/?item=105677
https://db.pandawow.me/?item=105672
https://db.pandawow.me/?item=105675
Druid
https://db.pandawow.me/?item=105676
https://db.pandawow.me/?item=105673
https://db.pandawow.me/?item=105677
https://db.pandawow.me/?item=105675
Mage
https://db.pandawow.me/?item=105676
https://db.pandawow.me/?item=105677
Warlock
https://db.pandawow.me/?item=105676
https://db.pandawow.me/?item=105677
Priest
https://db.pandawow.me/?item=105676
https://db.pandawow.me/?item=105677
https://db.pandawow.me/?item=105675
In-Game Version (Class: Warrior):
Characters who have already defeated Garrosh Hellscream before this change will receive this quest as well, so players do not feel obligated to bring new characters to receive the Heirloom they wanted in the first place.
Overall, I think this solution should satisfy the majority of players. For now this modification will be applied only on PTR later today until it's successfully validated.
Previous implementation will continue to work until the new one gets enabled on live servers.