I just checked my discover and saw that I do have a 0% BT promotion from them available. Unfortunately the issue there is that my limit is only $2200 so I would pretty much be in the same boat with high utl. Last time a requested a CLI from them it was denied 
@Bman70 wrote:
Call your current card providers and ask if there are any 0% BT offers available for you. It doesn't necessarily require a new app - BofA just gave me 0% until 2017 and I've had them for years. If they say yes, push your luck and request a cli.