Yes you are correct regarding dividing and spreading over a 3 year period.
The $2000 withholding will be applied to this years return independent of the repayment option you choose.
As of this writing your taxable income will be increased for the following two years and you should make an arrangement for that by increasing withholding or paying estimated tax.
-follow these links for additional information-
2020 Stimulus: Tax Relief for This Year's Taxes - TurboTax ...
Free Tax Calculators & Money Saving Tools 2020 ... - TurboTax
