Since July 1st is the halfway mark of the year you would add boxes 4 and 6 and report 1/2 as the non-Ma portion. The change of address will not affect this entry.
Not getting the residence changed will affect the tax withholding in the state section (Boxes 15-17) on your W2. However, when filing the part-year returns for each state you can allocate the correct amount of wages to each state based on when you actually moved.
So you may get a little refund from NY, but owe MA since the withholding will be off.
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