how does he do undersaddle when you ask for a canter? Will he canter then?
First make sure that you are giving him a big enough circle...the smaller the circle the harder for the horse.
If the lundge whip isn't working, try using something else. He can't be desensitized to everything...try an actual flag (one on a pole), try trying a milk jug to the end of the lundge line, use your imagination.
Sounds more or less that he is testing you because he really don't want to canter. You MUST keep on doing it until he does...if you give up, he's winning.
A horse I used to ride, no matter what we used he didn't want to canter...we ended up putting 5 large plastic bags on the end of the lundge whip, and if he wouldn't go we would give him a tap with it on his hind.
The worst thing you can do is just give up and let him trot all he wants...you are giving in to HIM. You want him to give into YOU. You must be the dominate one, you must be the leader were as he must be the follower.