When I upped my BC limit to $3,700 in May, I did it manually over the phone with them, to buy a new rMBP. They approved it, and actually let me make the purchase over the phone. I got the email while still on the phone that the order was processing, etc.
I'd just call them, and say you want to use your new CL to make a purchase over the phone. They can find you in the system and process it.