Advice needed on closing cards for Cap One, Citi, Bank of America, Discover, Chase.

I made a decision to close some cards in order to get the lowest APRs. I have not had luck on getting my APRs lowered any other way. Before I contact a NFCC company, I thought I would try one more time calling the companies but this time be willing to close the accounts.

I am wondering if I just call and say simply "Before I go to a debt management company through NFCC, I wanted to call and see if I could get a very low APR so I could finally pay off my bill." Then when they say No, I will say "I will close the account if I could get a low APR."

Is that what I should say? Is there a certain department I should ask for? Maybe the "retention" department who handles account closings?

Also I am wondering how many points my FICA will go down if I close multiple accounts at the same time. I am at 697 now with 91% utilization. I'm current on all cards and don't want to let the cards get past due. I've had the debt for years and really need to finally be smart about paying this off.

Am I correct in assuming that once my FICA goes down and multiple cards list that I am in a "financial agreement" with them (or whatever the word is), that my other cards like AMEX might close the card even if I don't have a balance? Would it be better to spread out closing the accounts over 6 months instead of all at once?

I would appreciate any experience you have with the following companies below on what you said and what was the drop in your APR that they offered?

Cap One

Citi

Bank of America

Discover

Chase

Thank you so much!