Live in NY, employer is in NJ

I am a full year NY resident. For 2022, I worked for a NY employer from Jan-Aug and then switched to a new job for a NJ employer headquartered in NJ from Sept-Dec. I work in the NJ office 1 day a week and otherwise work from home in NY. I know NY will tax me for the full year, with a credit for NJ taxes paid. 

For the NJ day allocation in Part II of the NJ-1040NR, should I just allocate to NJ 1 day a week from Sept-Dec? Or because my NJ employer is headquartered in NJ, should the full 5 day weeks from Sept-Dec be allocated to NJ, meaning my full NJ W-2 wages from Sept-Dec are allocated to NJ?  It seems like the day allocation would work in my favor if that is the right way to allocate. And in any event, it means more taxes would go to NY (my preference) over NJ if I allocate fewer days to NJ. 

Thanks!