If you are unemployed, have less than 150.00 in the bank, have a vehicle worth less than $5,000, and your house has less than 150,000 in equity, you are likely judgment proof (which doesn't make the calls and letters stop, but does prevent enforcement of the judgment by garnishment or sheriff's sale). You are past the "making admissions" stage if default judgment has already been entered: You have been found liable for the debt, so that ship has sailed. I see no reason you shouldn't write the letter yourself. The creditor is not likely to "dismiss" the judgment before getting paid, but you can request a statement from them in writing confirming that they will file a satisfaction of judgment when they are paid.
If you can settle it, great. If not, bankruptcy may be an option, or just waiting for the judgment to expire in 5 years (it can be renewed every 5 years, but collection agencies rarely renew them if there is no prospect of collection).