Get Your Butt Into Shape
This probably goes against what you've been taught about lifting. If you want to push big weight, you need to push with force. "Feeling the pecs burn" or "isolating the pecs" don't apply here. When that bar hits the chest, you need to lock it out fast.
Low reps build strength is what we were told. This is true but spending some time working with higher reps will help build strength and muscle. Instead of just hitting singles and triples, add some sets of five or eight to help build that pressing power.