In my experience carrying a balance seems to motivate CCCs to auto CLI. I got my Barclays Rewards MC in 4/12 w/CL of $2500. They auto CLI'd to $3500 in 9/12, when I was carrying around a $700 balance. Then they sent me checks with 0% interest for 15 months. I needed the short term loan and paid off my balance and used the checks to where I was within $50 of the CL. 
I made $50 payments when the minimum was $35, and didn't use the card so purchases wouldn't carry 22.9% interest while they applied my payments mostly against the 0% balance. The 0% was going to expire in 9/14, so in July & August I paid it off. Barclays responded by auto CLI to $5700. I've had similar exxperience with Merrick Bank, carry a balance for a few months, pay it off, and they auto CLI.
So I'd suggest you carry on as you are now for a month or two & see if they auto CLI. If not, then pay the balance off when you're close to loosing the intro 0% and I'll bet they respond with an auto CLI.