nah it doesnt sound like board presses will help with that, do you know how to use your lats and back when benching?
Try this without any real weigth, pull the bar down slowly(remember form, shoulder blades etc..) and really tense and feel the pull in your back like its a spring that your pulling together(keep it tigth all times) when the bar touches your chest start flexing your lats like your doing a lat spread, this when done rigth, should move the bar off your chest quite a bit, when you add the pushing muscles to this and you should have a new pr ready, i did when i learned this to a tee.
What i would do now is:
During this cruise take it real easy on the shoulders, tris and chest. Work on speed and form. (bench and pushpress)
Aim for a new pr during your next blast, a small one, even 5lbs improvement will do wonders for your mind and get you out of that plateu.
Use dumbells chest press as assistance. And mix it up, i like to do them with one hand at a time sometimes, as im sure you know the exercises that are the most ackward and hard tend to gives the most.
DO NOT go to failure before you try that new pr. Always 1 good clean rep in the tank. Overtraining is the single biggest reason why lifters dont improve, whether it be training to failure too much(i dont at all!) or too much volume. Im reminded by this constantly by thinking im not doing enough and end up overtraining, when i trust my program i always see improvement.
Good luck bro, dont get frustrated it takes time but it will come when you apply the work