1. Keep combat dynamic. If the player doesn't know what they're doing this round, skip their turn and move to the next person. They'll be prepared next time.
2. Offer bonus experience for people who keep their characters focused and play well. If they're on their mobile phone playing time waster games during combat, reduce their bonus experience since they're not involving themselves in the game.
3. Allow actions off turn. Typically I let my players shout advice as an immediate action during combat even if it's not their turn.
I'm not doing this right now since my group has some newer players in it (and thus they sometimes need a bit more time), but a adding a simple 30 second sand timer for "turn decision time" (including other player's advice talking) can sometimes really help keep the ball rolling by making people decide what they are going to do quickly or pass (we generally would say if you didn't decide in time you just automatically took the "dodge" action, but if you wanted to be a little harsher you could just say that their character stood there dumbfounded or something
).
For rewards inspiration (or other DM given small rewards) can also be a big push as was noted. Players tend to be a fair bit more likely to decide to do things quickly once they make the connection that doing so has a chance of rewarding them instantly with inspiration or something similar.
Edit: Funnily enough I'm finding a surprising amount of children's teaching tools extremely viable for use in D&D (little plastic squares as markers for things without figurines, larger sized sand timers than the ones you find in most games...
)