My sticking point is the same. I used to always be weak off the chest, well, a couple of inches off the chest but it's changed. Apparently the bar shoots off my chest now, even when I come to a grinding fail. I don't know if it's triceps or shoulders, but i'm getting my shoulders stronger and started getting my triceps stronger. Just hit both
Right now i'm doing 5-3-1. I need 5-3-1 right now because of my schedule, and i'm progressing. Military Press is one of the lifts, plus the accessory on that day is 5 x 10 military press (alternated with pull ups). After benching, I'm doing 5 x 10 close grip benching (alternated with chest supported DB rows). Next cycle, i'm adding some isolation for tri's something like push downs or a skull crusher variation (not decided yet). It's deload weak of my first cycle using close grip and military press for assistance, so too early to tell how much it's helped.
I would however love to train it a little differently, using bench variations like floor press and board pressing to zone in on the sticking points (and get used to heavier weights). This is actually how I "prefer" to train but I can't fit it in consistently right now. I would like to have a speed bench day, with every 2nd or 3rd speed day followed up with working up to a heavy single double or triple, plus an ME day using the special exercises (boards, floor, incline, close grip etc), with the assistance on both days hitting shoulders, back, tris, etc, with load of volume (Very westside barbell-ish, really).. I've done this set up before for different reasons with different weakness and also rotated speed bench monthly to swap it out for heavy back work (weighted pull ups, mostly). I only stopped this because I was spinning my wheels, not being able to fit it all in right now.
At the same time, though, 5-3-1 is working, so even if I could, I wouldn't come off it just yet anyway. I plan to stay on 5-3-1 until I stall then switch to something else (I have cresseys show and go in the pipeline, too lol).
btw, It could also be a technique thing. I've seen people drift towards their face far too much on the way up. This will screw with your bar path and increase ROM (so you'll run out of steam before lock out). Note that the bar will always drift a little towards your face but it shouldn't be excessive.
One of my training partners (i'm not always able to train with the same people regularly, so it chops and changes) does this, and we struggled to find his ideal set up and technique because his arms are about a mile long. He also had an interesting issue by tucking his elbows too much. And, he started the movement with the bar above his chin/throat, as opposed to above his lower chest. We brought his grip out, and got him bringing the bar above his lower chest before he started the movement, and a concentration on pulling the bar apart on the way down. Fixed his form, and upped his lift a little - nothing drastic but it seems to have broken a plateau.