My experience is (from last Nov and this Apr) is a BOG FP isn't very hard to get once you're 7 days out. The link doesn't seem to be very well-known, and it's not linked to the "real" FP system, so it's not like trying to get an A&E FP.
HINT: If you don't like the two times the link gives you, hit F5 to reload the screen, and it will suggest a new set of times. Keep going until you get a time you like.