You're a multiboxer, so you with a bit of work you can have a slightly easier time on the neutral AH than other players.
- First scan the AH on both factions for a week or so.
- Buy 11k worth of bargain price items that are likely to sell well on the other faction.
- Late at night park an alt at each of the neutral auction houses/auctioneers, so you can make sure no-one else is there to 'snipe' your auctions with an auction-botting mod (using one of these is bannable. The feature was removed from the auctioneer addon at Blizzard's request, but there are still people who use modified versions). There's one auctioneer in Everlook, one in Gadgetzan, and 3 in Booty Bay (By the bank, the exploding chicken, and downstairs in the building with the knife thrower). You can do this bit without multiboxing, except you'd either have to log out and in again a lot, or find some friends with vent/teamspeak.
- Trade items from one faction's alt to one on the other faction at 1c each, and avoid the 15% auction house cut. Easy Buyout in the auctioneer addon makes quick buying easy.
Or you could just wait until the faction change thing goes live.
Oh, and if anyone is on Alliance side on EU Eonar, I've got a gnome looking for guild signatures for <Horde Twink Supply Dept>.