I actually had an idea for this that might work, but you might have to pay a percentage for the transfer.
Bring both characters to Booty Bay and put something up in the Auction House there with the character that you want to transfer the money to. Put a grey item on the AH for a ridiculous price, switch toons and have the richer toon buyout the auction. It should work, but like I said I haven't tried. I haven't seen anyone else post on this method, and I hope it works for you. If not, trying it won't lose anything.
It works fine as long as the toons are on different accounts. However, the normal AH (in SW or Org) takes 5% of the sales price... the nutral AH (like the one in booty bay) takes 15%. To cross faction most effectively, you try to avoid the 15% nutral AH fee.