So far the amount of transmutation stones that you can get from all sources, that I'm aware of, are as follows:

First Random Dungeon of the Day: Green Geode (1)
Normal Pledge: Green Geode (1)
Vet non-HM Pledge: Blue Geode (1-3)
Vet HM Pledge: Purple Geode (1-10)

nMA: ?
vMA: 4
Weekly vMA: Blue Geode (5)
Normal Trial: ?
Veteran Trial: Gold Geode (1-25)
Weekly vTrial: ?

First "Rewords of the Worthy" of the day: Gold Geode (1-25)
7 Campaign End Reward: ?
30 Campaign End Reward: Gold Geode (50)


All of these are per-character.

As you can see the rewards are heavily weighted towards the PvP content. This isn't a bad thing, it's definitely a good way to attract more people to PVP, in particular BGs. However, the gap between the rewards you get for PvP and PvE are massive even before you consider the large difference in time and effort committed. An hour+ long haul through a HM veteran DLC dungeon gives 1-10 stones, seemingly weighted more towards the lower end whereas leeching off of a zerg for 20 minutes or completing 3 BGs gives you a Gold Geode. My suggestion is simple, slightly increase the rewards given from PvE content, particularly dungeons, while still leaving PvP rewards the way they are to better reward players given the time they spend. Specifically I believe that the "Random Veteran Dungeon" option should give a blue geode upon every completion, or at the very least a green geode. This would importantly incentivize players to use the Random Vet option which is often neglected due to lack of rewards, additionally it would increase the total population of people running "all" dungeons and should help alleviate some issues people have with queue times. Similarly, it might increase the amount of healers/tanks available in queue; in my personal experience I have a tank Alt, geared well enough for vet dungeons but not for trials, whom I hardly play simply because I no longer need to farm dungeons. This change would greatly incentivize me to hop on that tank alt and run a few random vets each day when I need transmutation stones.

The second change I would make is towards DLC dungeons, where effort clearly does not meet reward. At the very least, veteran pledge completions of the DLC dungeons should give purple geodes and HM completions should give gold geodes. A simple survery showing the number of players who even have the HM completion achievements for the DLC dungeons would show why this is necessary. It might also be worth considering to make every completion of a veteran DLC dungeon (or any dungeon deemed "harder" than usual) gives 1 stone outright; this would fix the "potential" problem of people abusing the "random" change I suggested by not owning any of the DLC and always getting easier dungeons. Simply reward more for more difficult content.

I've always enjoyed doing dungeons in MMOs, even if I've done them hundreds of times before, however the staunch lack of rewards has put me off from attempting them further, and lending my help to less experienced players trying to finish them. I thought that the transmutation system would give me a reason to go back to them but I'm finding that I can just spend half the time for double the rewards and get "Worthy" rewards on all of my characters.