Just to add a new datapoint (albeit a few months later), after having no luck in the entire last year booking any TK business awards from LAX to Europe (for every season), I've been finding some random availability for my upcoming trips and was able to book an outgoing flight for Thanksgiving. I could have booked another flight for March which I didn't take up since I already had a flight booked on another airline that I didn't feel like canceling (have to pay a fee). Availability is still very sporadic but there's a bit more reward for frequent checking. I have three trips to Europe between Thanksgiving and next summer so whenever I had a few min, I would go in and check all the possible dates.