is it possible to negotiate back taxes debt owed to IRS, using a donation this year to offset past years' debt?

Unfortunately the IRS will not reduce a tax debt based on a later charitable deduction.  In fact, when determining your abiliity to pay under an installment agreement the IRS limits the expense that can claimed for charitable deductions. While it is honorable that you would like to make such a generous charitable donation, if you have an asset that is worth $50,000 then it would most likely be prudent to liquidate the asset and use the proceeds to settle with the IRS. Best regards, Adam Brewer