Sure, you can ask them for a PFD.
Is it a 3rd party CA or in house OC collection?
Settled or paid in full looks the same to FICO and won't hurt your score. Where it could cause a problem is on manual review.
You could ask them if you settled to report as paid in full if they won't do a PFD.
You have a golden carrot to dangle at them and attempt a modification of your existing agreement.
I would offer them full payment now in exchange for agreement to delete from your CR.
Satisfaction of the debt prior to mortgage app process is definately a plus, with or without CR deletion, as it is hard to predict what requirements your prospective mortgage lendor might impose. They may, even though you are under a payment plan and are making satisfactory payments, want the debt satsified in full prior to loan approval.
If you can also achiever CR deletion, any part that your score may play in the mortgage app process, such as getting you a lower rate, will be a plus.
If they accept a PFD, I dont see that you need any letter of zero balance, as it will no longer be on your CR, and thus not somethng the mortgage lendor will even be aware of.
That is the best of all options.
Congrats! Be on the watch for the 1099-C on the $3,000 for next years taxes.
When you do get the 1099c, check out your obligation to pay before simply paying.
If you can show insolvency, meaning your debts, including the cancelled debt, exceed your assets, you have no obligation to pay taxes on the cancelled debt.