"Does the IRA distribution count as income in that calculation?"

The instructions include starting here:

"LINE 1 - NEW YORK STATE TAXABLE INCOME

If you file NYS Form IT-201, enter the amount on line 37. If you file NYS Form IT-203, enter the amount on line 36. If the amount withheld pursuant to Section 1127 was included in itemized deductions when calculating your New York State Personal Income Tax liability, you must add back that amount to the amount from line 37 of NYS IT-201 or line 36 of NYS IT-203, as applicable, on this line."