You might need to work on your technique. I love this Dave Tate video about it but be warned it is not work and family safe due to language (it's Dave Tate...)
Other than that you will probably want to add in more heavy bench work and other accessory lifts like board presses. And I am not totally clear on what you are tested on, are you saying it isn't a real bench press but a machine where you start from the bottom? If so that is quite silly but if that is how it is then that is how it is and I would focus on benching in a rack where you can start from the bottom with pins set.