As a lesson horse he probably developed a "hard mouth". He's probably had tons of people lugging on him and just gotten used to it. Alot of times a horse will actually get used to the rein preasure and use it as a "third leg", or extra balance.
You could go out and buy a slightly harsher bit, but I wouldn't really suggest that as you could more than likely just go back to the basics and reschool him.
I would do alot of downward transitions, get off the rail, do serpentines and circles. Go from a walk to a trot and then ask for a halt, immediately back and then go back into the trot. Change directions often and when you go to canter, only do it for a few strides. Maybe 5 and come back down to a walk or a trot.
The trick is to get him paying attention to you, you want him wondering which way are we going to go and when are we going to stop. Do some gymnasics, trot and walk poles. I'd drop the jumping until you get him listening to you better. It's not going to happen over night but eventually, a light bulb will click and you guys will be a team.
"Be a best friend, tell the truth, and overuse I love you
Go to work, do your best, don't outsmart your common sense
Never let your prayin knees get lazy
And love like crazy"