Actually what i think has helped me alot also is building up the back like crazy. Ive been really working on that the last 5 months and i have never felt more stable on the bench. Im sure the extra tri work has helped too.
reverse grip also helpful, and once you get used to it you can go surprisingly heavy. Also really pumps up tha gunz
I know Jim swears by OHP, especialy standing, but I don’t personaly make enough progress on it. bench, deads, squats I can continue to make progress month to month, but not on OHP, so for me I can continue to make progress on 45 degree incline for 531 lifts, and do my OHP as my BBB after incline work. Then every few months I switch it up for a cycle or two, doing OHP as my 531 and incline as my BBB. This works for me, I don’t tell anyone else how to design they’re own workouts, but my OHP gets stronger this way, then if I only did OHP’s, and left out the incline work. Thats my story and I’m sticking to it 
It all depends on the person. I do both OHP and Incline BB and as they go up (along with flat DB and Dips), my bench goes up. I know people who don’t do incline, people who say its the best assistance exercise and a couple guys who have a huge bench without doing either. You have to find your weaknesses and try to diagnose them with with exercises you think work. From there it will take time to figure out what works for you but you will start to fine tune your accessory work to what feels like its helping you the most.
To answer your question, for me, Neither improves my bench. When I benched with a wide grip, pointer fingers on the rings and had my elbows out gym rat style, aka barbell flyes and touched high on the chest, Incline benches did me pretty good in terms of helping my flat bench. When I pulled my head from my ass and learned to bench properly, took a narrower grip ( pinkies, maybe ring finger on rings) with elbows at a 45 deg angle to my body and touched at the sternum, heavy tricep work was the best thing for me. OHP did and does shit for my bench.
Flat bench only. Use a slingshot. Do half reps (chest to half way up) and keep the pressure on the bottom portion. Pause and press the last rep of each set.
I’ve NEVER found “carry over” in any other movement. Just bench and adjust your frequency and intensity. Cut out all the extra crap for a while. Focus on technique and recover quicker.