I have always managed to book SkySaver awards online - have never needed to use SkyChoice. I am usually pretty flexible with my travel schedule, so that helps.
My most recent awards were ATL-IAH in September - I booked about 5 weeks in advance and got my preferred days and times (coach). Just got back from ATL-LAS over Thanksgiving with the family. Booked 2 seats in First with the desired outbound - had to settle for the redeye on the return (but still in First and all SkySaver - booked about 7 weeks out). ^