How do you change regions with credit on your account?

If you move and have credit on your account, you cannot change regions.

Apple suggests you spend your credit, and then change it. Well, I have less than 0.5 USD on my account, there's nothing I can buy with that (not even a song on iTunes).

The next suggestion is to add a credit card or payment method so credit can be spent and 'extra' simply charged to the card. This is fine and good in theory, but my cards are not accepted because... you guessed it... I can't change the region.

So I can't change the region because I have credit, and I can't spend that credit with an additional card since my cards are from another region. Catch-22 anyone?

I might add, this run-around is to be able to buy new apps in my new area, but given these hurdles I very much feel like giving up, and spending no money. Seeing as people do move around regularly I can't believe this is so difficult.