Not sure stronger bitting is the answer coz there is a reason for him rushing. Schooling is required! Getting him to respond to your leg, seat and hand both for sending him forwards and bringing him back to you.
Wait for your instructor to see the problem with her/his own eyes.
yes teeth and back ok _ read old posts of mine!! (was issue last year and still has regular physio)
His schooling is fine off the leg soft in my hand works through his back. We have only been at new yard just over a week and he seems very excitable (we he is very excitable) and keen . Friend who watched though he was a bit over bold as the jumps were quite small, raising them really helped buts not the answer> Never normally change bit hence the lack of them. He is fine on landing its 2 strides away from the jump he moves up a gear or 2.