As an elite, one of the most valuable pieces of information you're likely aware of are the upgrade windows. If you can't secure a bulkhead or exit row during booking, keep a close eye on available seats starting at 120 hours before the flight. The elites that do get upgraded will often be occupying the best seats which are now free for the taking.

ExpertFlyer (a paid service) offers a seat alert feature that can alert you when specific seat(s) become available, assisting you in your effort to nab the spacious seats.