Now that Blizzard is making the heirlooms truly xrealms, is it not odd, that suddenly they have the tech to do it In-Game, via the mail tool?
Honestly, I think they could have done it for a LONG time, but it just has been too good source of income to them.
"In the latest 5.4.2 PTR build, we are testing the new ability to mail account-bound items to other characters on your account that may be on different servers. Notably, this should allow you to move heirlooms between servers, in advance of our planned Warlords changes that will make them fully account-wide.
Sending this sort of mail should work like any cross-server communication: You send the item to "Playername-Servername" and it should otherwise work like regular mail. Note that you can only send account-bound items, and not other items or gold.
Example: I have a character, Thrall, on the Benedictus server. I want to send my heirloom mace to my alt, Durotan, on the Lycanthoth server. I'd log in as Thrall, and attach the mace to a mail addressed to "Durotan-Lycanthoth" and hit send."