Heres another trick for increasing the returns we get for Conqueror Shards. This one comes from the quest rewards available after the end of the Maze Engine quest line.
The pic below shows the entire campaign. At the top is 'Defend the Sword Coast', which returns Gauntlgrym Bounty after 5 dailies. Out of that we can get 10 Conqueror shards.
The Defend the Sword Coast campaign task only takes 10 seconds to complete, and consumes 5 'Tales of Adventure' to do it. Those Tales of Adventure are a campaign currency that builds up by doing the daily.
Heres the trick: Don't run the Defend the Sword Coast task until a double shards event, (there was one on 12/25). Save up all your Tales of adventure until then, and it won't even take up any inventory space to do it! Opening the Gauntlgrum Bounty chests during the event will give 20 shards each instead of the normal 10.