For Nitrogen, it would be more effective to broadcast at the time of or a few weeks after seeding. For Phosphorus, you would benefit from mixing it into the soil profile since it does not move well in soil. Mixing will distribute it evenly to whatever depth you till, whereas broadcasting on the surface will leave a higher concentration at the surface that declines as you move down in the soil. Potassium is more mobile, but would also benefit some (but not as much as Phosphorus) from mixing.
Any Nitrogen you add now will be gone by 2 months unless it is some form of long release Nitrogen. If it is stabilized Nitrogen, how much is left at 2 months will depends on the specific type of Nitrogen used. Phosphorus applied now will almost all stay until it is used by plants. Over months, the Potassium will also stay in the soil until used by plants.
How much difference it would make to add now and mix is an open question, though mixing probably helps some for P and K. You can get excellent results from broadcasting Phosphorus and Potassium, so whether the extra work is worth it is a bit unknown.