Technique wise there is one major issue that will effect you off the chest. You are getting loose and letting the bar sink into your chest too much. This technique “works” when you incorporate a heave with the legs all through this is not recommended as if wreaks havoc on your back. When benching the style you do, it is best to keep complete tension on the chest, barely touch, but touch and drive back up.
A variation that can help teach this is paused pressing against bands, the pause forces you to stay tight, the bands force you to stay tight and force you to accelerate off your chest more than you would with straight weight.
Assistance work for this area would direct tricep work. JM Presses, DB rollbacks, Tate Press, etc. Things that you can hammer the triceps with but don’t give the shoulders a chance to take over.