Hi.
I would definitely agree to pull your Fico scores first. One thing to check is how many "hard" inquiries you have because that is a major factor for denial. If you really want a BBRZ card I would definitely check to see when your hard inquiries will "fall off"- for instance if you got all those department store cards all at once all those inquiries are probably still on your CR.
Once they fall off then reapply and you'll probably get it- only bad thing is you have to wait a few months to a year. IMHO
Another observation is I notice you already have some decent CL so I wouldn't worry too much about having to wait. I have also read some people here who have good luck calling the credit card company directly. IMHO
Hope this helps!
TU Fico 736 EQ Fico 730 (December 2012)