We went during the slowest week of the year (8/30-9/10) and FOP was easy to grab with a refresh session. I have to assume if you are very persistent about refreshing you could grab it then as well. Your biggest obstacle is current FP+ times. I always did it as we were leaving our morning park (noonish).
Good luck but not having it scheduled in advance just means you need to start refreshing a few times the night before and then religious the same day. (night before because people change park plans when they get back to the hotel or on the bus at the end of the day).