Frankly, I have no problems using my FFN's, even at the top properties. I just booked last week at PH Tokyo and PH Sydney for 4 nights each. Granted, they are all midweek stays.
My experience is that towards the end of the FFN period, the weekend nights (Fri/Sta/Sun) always fill up, but the weeknights are relatively open. This is partly due to the 3-night minimum charge of any awards in Hyatt, which works to my favor in this regard.
I regularly put award rooms on "hold" using my points without any regard to FFN period. Then later, if FFN is announced and that the property decides to offer FFN, I simply switch my points award reservation to FFN. Simple, easy and quick.
As a diamond, you should have no problem getting FFN's anywhere (less the Highlands, which is overrated anyway) at least on a weekday stay, even this late. If it helps at all, there's availability of 1 room for the entire period of 3/8-3/11 at the Park Paris Vendome.