Declaration cards: everyone gets a stack of six or so cards with various action categories on them: "melee attack" "retreat" "cast spell" &c. Reveal all at once before initiative is rolled. Makes combat fly by. Which is critical when you have 16 PCs and their henchmen.
Assuming and maintaining genuine control is the way to go. Keep the action moving,keep the campaign/adventure environemnt reacting to the actions of the players... don't try to restrict. The more players you have the more points of contact the players at the table have with adventure/campaign. The "me me" show reduces as players develop and improve their relationship to the adventure/campaign.
Sometimes I think Matt Finch's greatest skill is "DMing from Chair".
Stephen Chenault ran a number of games at GaryCon last March with 15+. Tactical positioning seems to be the common factor. Stephen used a U-shaped table setup and GM'd from the middle; running back and forth like my hyperactive blue heeler pup. It was the first table that big I'd played at that didn't use a caller.