Glad you're on top of this already, because I had exactly the same thought as clansing: I did see the hint about the New Year's party being on Sunday, but a party on the night of the 31st is (in my dialect? I don't know) a "New Year's Eve party"; something called a "New Year's party" sounds like something you'd hold on the day of the 1st.
(So it should just be as simple as specifying that it's a New Year's Eve party.)
That aside, I enjoyed the deductions and the clues!