re: when to pay
For the safe harbor described above (100%/110%) of prior yr liability the timing of the income does not matter as long as the quarterly payments are timely.
If your lump sum extraordinary income had been later in the year you might have been able skip earlier estimated payments. See https://www.irs.gov/pub/irs-pdf/p505.pdf page 25 "Annualized Income Installment Method"
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