Post author here. We did work out a repayment plan for some taxes. Payroll taxes are generally "if you have the money in the account, you have to pay immediately" though, so we wrote a large check for those as soon as we discovered the error.
What didn't make sense to me about that story is that even if their payroll system wasn't submitting the tax payments to the IRS, it seemed it was witholding the tax on the payroll. So the money was sitting in an account somewhere, they should have had it available to pay all the back taxes. They would only really be out the penalties, which could probably have been negotiated down on the basis of an "honest mistake." Though he did admit to sloppy bookkeeping overall, so maybe they saw all this money in the bank account and spent it on other stuff.