Are you benching raw or in a shirt?
I bench raw, and one of my go to moves are the floor presses. They directly translate to my bench, and help get the weight out of the bottom. I like to use a modest weight, around 65-75% of my 1RM. This weight lets me work at higher reps and focus on technique and generating the power out of my tris.
I also use a closed grip dumbbell press to hit the tris. If you have hex dumbbells, they work the best, but any work. If you lie flat on a bench with the dummbells on your chest and palms facing each other, you can hold the dummbells together (touching). I focus on keeping the edge of the dumbbell closet to my face at my nipples or a little below, and driving straight up, which almost feels like i am pushing the weight towards my feet. This is a great move to go heavy. But it is also good to use for speed reps to get a sick pump. The limited range of motion really forces the triceps to continually work without assistance from stronger muscles.
Get your reps up with rope pushdowns to relieve some elbow stress.