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Thanks for the feedback everyone.
I think I'm going to stick with Cap One for now and see if I can earn their trust more. Maybe I can get them to give me more credit - I'll just let Netflix bill to that account and set the auto-pay up to pay the account before the statement closes. Those three collections begin falling off next year (one of them remains for a few years) and I'd really love to get them dropped sooner than that.
I think at this point, I'm going to consider myself lucky as hell that AMEX and Discover let me in their clubs. Until then, my butt is going into the garden for a while!