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You'll want to get the balances down as quickly as possible so no high balance clock starts that would lead to balance chasing. If they already have it in the background to do so. Not much to do but plead your case why the balances were high. But lets think positive. Pay them down and get some points back for now.
I would think there would be less chance of being balanced chased if they got paid down sooner and not increments if you are able, but not sure. I've never been chased so I don't have any first-hand knowledge. Might want to look add some small loan or SSL to fix that mix. When I only had loans( and a quite a few baddies too) and then added a card, then I jumped between 40-50 points across the 3 CRA's. I'm not sure if going from 0 loans to 1 would be the same as with cards or not, but I'm sure its good for a few points. Getting those balances down and a loan would likely be good to get you in the high 6's if not 7's
It's easy to check and see if balance chasing is about to happen
Make a larger payment and see if your limit changes. If it does, it's hard coded and it wont stop till lender decides so.
Sometimes it stops on it's own, other times it keeps up till the account is closed.
I would be more concerned with Amex than Chase, so test waters with amex and see what happens
If they do start with balance chasing, I suggest you call and find out if there is any particular amount you need to pay for it to stop.
If that's an option, Amex rep will inform you.
Chase, while as prone to balance chasing as anyone loves the interest payments, so if you can get that balance down, you can probably save that card