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With the negs removed, definitely. They like thin files.
Someone correct me if I'm wrong, but if the OP has Charge Offs in addition to late payments on his credit report, removing the late payments really won't do much for his score at all as he'll still be in a dirty bucket with the presence of other baddies still on there. The major score increase you get is when you move from dirty to clean. There are dramatically diminishing returns when you are talking the presence of several negative accounts.
My EQ score (clean) is 77 points and 90 points higher than my TU and EX scores respectively because TU and EX each still have one dirty account.
Don't be discouraged. Having all that removed still looks good on review. Also, your most recent late is on an account that you are an AU on and it also has 20% utilization. You stated you have your own store cards. Is there a reason you are remaining an AU on this account and leaving it on your report?
I got approved for a Discover It, $2500 SL, last month with a 2014 BK and at least 6-7 CC and mortgage accounts included in it, plus a 4-month stretch of lates on my student loan in late 2013-early 2014, so if I did it, you can too!