I forgot to mention that Chase will allow you to pay toward pending charges. That'll speed things up a bit.
Also, if you want to report a low or zero statement balance, use your credit card to load up your Amazon gift card. That way, you still get your 5%, and you can make a few purchases at statement time without affecting your credit card balance. I find that $50 to $100 is more than enough on the gift card. A larger purchase can be delayed a couple of days.
I'm betting that if you do the right combination of using the card and keeping your balance in check, you'll get an automatic limit increase somewhere between 3 and 6 months. Mine came at 4 months. A friend thinks her increase came at 3 months, but it might have been 4.
