I bank with Chase and few years back I got to know one of the CSR's just from going in so often and asked about getting a credit card, he told me that they look for a minimum of 640 to qualify, he was an assistant manager. So you could probable get it although YMMV. He did not say who they pull, I know for my business GM Chase CC they pulled experian and they just approved a CLI recently and did a HP on experian again. FYI
Your util is way too high to be realistically approved, so I'd say the odds are slim to none. This is doubly true given your FICO is already substantially below what Chase normally looks for.
You have some tough decisions to make ahead of you, and like SwiftTone mentioned, gifts for Christmas are a low priority and should be reconsidered given the financial situation you're in.
You need to bite the bullet somewhere, otherwise you're stuck in a chicken and the egg scenario. You can't get approved for a low APR BT card because your util is too high, yet you can't get your util down because your spare money is going on higher APR cards that you currently have. Breaking the cycle will require an increase in income, decreased expenses, or both. Shuffling balances alone won't get you out of this situation.
I agree you don't have a good chance of getting approved for a Slate. I know it sucks, I'm sorry. I've been in that awful loop too, where you can't get lower interest transfers because your utilization is too high, and you can't get the utilization down because of the interest you're paying. A few ideas:
1. Definitely try for CLIs on your existing cards
2. Throw any extra money at trying to get all cards under 90% utilization. Your Citi and Cap One cards are considered maxed out right now, which is a big negative. Getting them at least under 90% initially should give you a bit of a score bump, and remove the red flag of having a card maxed out. If Amazon is only $400/$2,200, just pay the minimum and put anything else toward the Cap One and Citi cards.
3. Leave Care Credit alone for now, except for the minimum payment, since it's at 0%, BUT make SURE that it's paid in full before the 0% expires, or you'll get hit with a ton of interest charges.
4. If things are really getting difficult to keep up with on the credit card balances, you might think about checking your local bank or credit union for a personal/debt consolidation loan. You might be able to get one with a lower interest rate and fixed payments, which you should be able to pay off a lot faster. This can be dangerous though, because if you run those credit card balances back up afterward, you could be in a bunch of trouble. Also, talk about your possibility for approval with the bank/credit union BEFORE applying and taking the inquiry, if you decide to go that route.
As far as the skipping christmas/birthdays I would like to clarify that we are not going to be spending crazy amounts on presents for this stuff but we aren't going to ignore them either. Two of the birthdays are for my step-sons who live with their mom so there will only be a few gifts there. One of the birthdays is my daughter's second birthday so once again we aren't going to be crazy spending there (she really only cares about opening the presents v. whats inside) and the fourth is my soon to be 15yo step daughter who knows well enough about our financial situation and isn't expecting a lot there. same goes for christmas with all of that.
I plan on trying for CLIs towards the end of November or early December since (from what I hear) some creditors can be a little more generous around christmas time.
Amazon is on 0% interest also until December and is the highest regular apr so I will still probably try to get that paid off first. citi is the next highest apr and capital one (surprisingly) is the lowest. And as far as the CareCredit there shouldn't be any problems there. every two months we have braces payments put on it and get 12 months at 0% on a balance of ~$330
I was not dead set on apping for the Slate just wanted some input and you guys definitely gave me some to go off! Thanks =)
EDIT-- as far as the inquires I know that I have way too many right now I would like to say thank you to the sleezy used car salesman for that who was suppose to run mine and DH's credit each once for in-house financing and before we even got home I had alerts from citi identity for multiple new HPs I ended up with 15 across all 3 CBs and DH (who had no score at the time) ended up with 8 accross the 3
Don't worry about the car inquiries. They should only be counted as one inquiry in your FICO score, since they were for a car loan and all on the same day. That's also pretty easy to explain if you need to try to recon a CLI or app denial. It happens pretty much any time you let a dealer (new or used) look for financing. It's really other inquiries, like for other credit cards or loans, that tend to be an issue.
Definitely get the Cap One and Citi cards under 90% ASAP, regardless of the interest rates on them. You get a pretty hefty ding to your FICO score for having a card with more than 90% utilization, and more so if there's more than one of them. Once they're under 90%, then you can work on paying off balances based on either the size of the balance or the interest rate.