How old are the lates? Do they fall off in 2020, is that why the lender wants you to wait?
You can continue to write GW letters you may get lucky, but just because they are paid (which is great of course) does not mean the lender will remove them . Some lenders are very strict and refuse to remove. I have lates from 2012 that will fall off end of this year, chase refuses to remove lates after about 20 GW attempts.
I am not trying to be harsh, but realistic. Derogatory information on your credit report is not there to serve as a mechanism for repayment, but rather an indicator to future lenders of your overall creditworthiness. Because the past debts are paid does not entitle you to the removal. I believe creditors are not supposed to delete information because it is paid.
Others can provide more insights to how best to try to have this removed.