Are transmute shards bankable? If so that will be limiting me to playing only on my crafter which is no bueno.
You get a reward container called a geode. This is bound to character.
When you open that reward container, you get crystals. These crystals go into an account-wide reserve (holding up to 200 crystals) that is not in your bank or on a character.
So your characters can get reward containers, open them, and your crafter (or other characters) can use them without ever touching the reward containers themselves.