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If they are 30 or 60 Day lates, they aren't doing much damage to your score at this point. If any are 90 Day or more late, they'll still be hurting your score by 50-80 points.
Your best course of action would be a GW letter campaign stating that you've been on time ever since and would they pleeeeeease remove the lates? Good luck!
It's not the range that matters. It's the actual number assigned to each Late. So your worst Late is 60 Days.
+1 to attempt to remove the late payments through GW letters, I had success with Capital One, Credit One, and other creditors. The fact you have new accounts with these creditors in good standing should help, and be referenced in your GW letters.