Two things have helped me to be stronger off the chest... OK 3 things: 1) Getting a better arch is one (but if you aren't a powerlifter this may not matter to you), 2) Doing reps with a pause on the chest and then trying to explode the weight off your chest, and 3) Pin presses at chest height.
I imagine your upper-back could be an issue too, but without seeing your form or anything that's tough to say.
I am probably not the best person for bench press advice, but these things do work and they helped me go from benching 200 to 265 over the course of 1 year and my issue was power off the chest as well. Give it a shot and see what you think.
Post some video and maybe someone more knowledgable then me can help you out.