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If your history with Capital One is clean, your best shot at a high limit is a Venture, but I don't think they have 0% intro rates on that card. A Venture 1 or Quicksilver does have 0% intro, but based on what you've shared I would guess you'd get maybe a $3k limit on those. if you have any derogs with Capital One I wouldn't try it.
I feel like you would have a better chance at a higher SL through a credit union. I've heard good things about NFCU. Amex can give decent SL's, but it all depends upon your profile. Both my BCP and ED card's started at 5k.
I have seen 3.5k limits with BCP, so I don't think there is much between BCE and BCP for SL. The good thing about Amex is that they grow fast.