"Can I pay the increase in taxes due to the NUA in my final quarter estimated tax payment and not spread the increase over the entire year?"
Yes, but to avoid an underpayment penalty you might need to annualize income on Schedule AI of Form 2210 to reflect that the income was received in Q4.
Form 4972 is for calculating the taxable income to be included on your tax return. It has nothing to do with when during the year the income is realized or how or when you pay your tax liability.
