Do warmup well, working to the heaviest weight , doing half reps (with less than by the book form ) may be a start to increasing shoulder girdle strength. Including 4 to 5 inch partial reps at the lockout position. Add the Press Behind The Neck to the workout, which many top benchers do. The only other overhead press you might alternate with are jerk or push presses. Try working out only twice a week on any pressing (flat/incline/overhead) movement. Try not adding this or that exercise, just stick to the basic stuff, for now. The exception being, the weighted dip. Only an personal view, but I consider the dip a better upper chest/upper body/triceps movement that the bench.
People have given a lot of good advice since July. Most BB'er would have added at least 20-30lbs to the bench ,for 8 to 10 reps in a normal workout, by now. Not being critical, just factual, judging by some of the lifters I have been around. Not everyone is equipped for big weight in the bench. Lot of massive pecs/chest built with 220 to 240 benches for BB'ers. And than again, 400lb+ for some high school kids, who are just naturals for that lift. Still can't figure out way so many BB'ers seem obsessed with the weight they use on the bench. For a pure BB'er, it should not be that important, but exercise performance is. Good luck.