Yes, that all sounds correct.
New York has an unusual rule that W-2 box 16 must be the same as box 1. Any adjustments are made on the New York tax return. That's what your allocation does.
You should allocate your interest income based on where you lived when you actually received the interest or when it was credited to your account. That's not the same as allocating the total for the year in proportion to the amount of time you lived in New York. Any interest that you received before you moved out of New York is New York income. The same applies to pension and Social Security income.
You should be filing a part-year resident return for New York.
