This won't work for everyone, but I kept getting annoyed trying to keep track of transferring money back and forth to the US and it was becoming a big logistical nightmare for me- so once I was able to build up some credit history here, I took out a loan from my bank, did 1 large wire transfer and paid my US credit cards off completely. The debt doesn't go away it only transfers, but now I only have to worry about paying 1 loan and I pay it in a currency that I make money in, so I'm not subject to the exchange rate- and the best part is, the interest rate is way lower than it was on the cards.
YMMV