1. There is no way to "negotiate" the tax issue. If you settle a debt, and the unpaid portion is more than $600.00, the IRS code (law) "requires" the reporting of the forgiven debt income. That issue is not part of the settlement. You either qualify for an exception to paying tax or you don't (e.g. insolvency exception, bankruptcy exception, etc).
2. As for credit impact. You can try to negotiate a "pay to delete" type of arrangement. Meaning once the settlement is performed, they delete the account from your credit. However, actually getting the creditor to agree is rare. Mainly because it is not worth it to the bank because credit reporting is largely automated, so someone has to manually change it which is more hassle than you think. But no harm in asking.
You didn't mention if you were trying to settle it just as to you, or settle it for all borrowers. If you only settle as to you, that still leaves the other signers on the hook.
There is no way to obtain a minimization of either the tax or credit impacts. On the credit side, your credit is already hit with the default being reported. Unless you pay the debt in full, they are going to continue to report (lawfully, I might add) that you are in default. And, on the tax side, unless you settle for less than $600 difference between what is owed and what you agree to pay, the unpaid/written-off balance WILL be reported to the IRS absent something like a bankruptcy filing.
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