If it were me, I'd begin the booking process, find a fare/schedule/airline that seems reasonable. Go so far as to view the seats available. If only a couple left, book it. If lots of seats, hold off. Repeat every couple of days. Sometimes pretty amazing to see seats magically appear that were not there a week before.
Be sure to clear your cookies too as those airlines can be sneaky and not always show you the best fares, if they can tell you've been "shopping".