If you’re willing to take the AH cut, you can send gold to your other-faction alts by having a friend’s account make an alt (as the same faction as your alt) and put a gray item for sale for a really large gold amount (100,000+ gold or somesuch). Then you buy the gray item on your main and have your friend give you the gold.
Obviously it requires having a trustworthy friend with an active account, but I’m sure you can scrounge someone up.