There is no quick fix for this situation. I am in the middle of a similar situation. It just takes time to develop a payment history with your new cards.
Just take it slow and they will raise your limit. Also if you get an offer for a better card in the mail do not hesitate to take it but be sure to cancel out the old one and then tell them the reason. They just might surprise you and give you a higher limit to keep you as a customer.