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Disclaimer, I don't know if SLs are subject to EE but in general
TU, six months. Call and ask for supervisor. Usually goes without a problem.
EX, three months and they are treated as a dispute. It works for some people, for others it was an epic fail. So, it would depend on your risk tolerance and if 3 months are worth potentially crashing your score again
EQ one month. Don't. Just don't. Really. Don't.
You can try GW letters, I guess the success would depend on servicer. At least you know late(s) will be gone soon, and now that it's paid and closed, there wont be any more updates.
21 year old me would probably kick me
Just FYI: EEs are a lot harder to get for lates than they are for derogatory account removals. If the account is otherwise in good standing (I'm assuming since it's paid, it is), I would leave it alone so that they don't just delete the account early (positive accounts can stay on your report longer).
You can try to goodwill them, and you have better odds because the account is paid, but you are right - Nelnet is not easy about giving goodwill adjustments.