How old are your other cards? What you would do is add the age of all accounts, then divide by number of accounts. Do this "without" adding in the AU account and see what your AAoA comes up with and how much impact deleting the AU would have. The greater your AAoA, the better.
From a purely FICO score standpoint, if the AU is one of your older accounts and deletion will ding your AAoA down very much, you should leave the AU account alone. With the "late" crossing 4 years ago in just 6 months, the late as a derog will begin to have less effect on score than the positive age of the account and more its recent positive history.
With that said, you must realize that FICO alone does not decide credit. While a large percentage (90%) of major lenders use it, it is only part of their decision, not the deciding factor. And some lenders do not use it. Some lenders will "prequalify" you with score, then decide on actual approval or amounts based upon your content. Some items, such as BK, collections and other "major derogs" are deal breakers for some lenders. BofA is very hard on major derogs, especially BK.
A 30 day late, 4 years ago won't be a deal breaker most of the time. But it can influence some credit decisions.
As for the $2K, I would pay off all of the small balances, then don't use them or at least not more than you will PIF each month.
Then I would use any left over on the larger account and then make a major attack on the larger balances with the $400 per month and snowball up from smallest balance to larger....meaning make your minimums (plus just a little) on the higher account and put your full force of extra principal on the smaller.
My rule of thumb is always try to pay at least a little over minimum on accounts. Paying the bare minimum shows that you are maxed out not only in credit but in income and ability to pay and that you cannot handle any additional credit. When you pay in bigger chunks, both over a few to several months, it shows that you have discretionary income or at least the ability to more than manage the level of credit you have. Transferring balances, establishing new credit, etc. does not. In fact some lenders may view it as "robbing Peter to pay Paul."
Anyway, to make a long story no longer than it is: get the number of accounts with balances down. Pay more than minimums, but focus the majority of extra principal on the smallest account and snowball upward. Don't use more on the cards than you can PIF while you pay them down. Any new use, try to make sure you pay it before your statment cuts off so that you do not have new balances settling on your account.
Ideally you would only have 1 or 2 cc's with balances in addition to your auto or student loan and the utilization would be under 10% for max utilization points.
With this strategy you also avoid additional inquiries and "new accounts." If you are considering a new account, then you might as well consider deleting the AU account.....both will lower your AAoA, but deletion of the AU account will at least improve the "content" of your report.
No easy or short answers. Common sense, conservative use of money and DON'T SPEND credit, utilize it within your financial means.
