It might not be that FDP are sold out...it could just be that Sci-Fi itself is booked. Disney doesn't set aside reservations specifically for FDP, so this happens when FDP are released so late: by the time FDP are released, the most popular restaurants are already fully booked. Do you already have a regular ADR at Sci-Fi? If so, you could open two browsers and log into
MDE on both. Have FDP pulled up and ready to search in one browser, then cancel your regular Sci-Fi reservation in the other browser. An FDP SHOULD then show up, but it isn't guaranteed, so there's a risk.