One of the most effective ways to stabilize the shoulders, hips, and spine during heavy horizontal pressing is by training the bench press in reverse. Start the bench press with the lifting phase, NOT the lowering. How? By pressing from pins.
The Banded Barbell Pin Press
Place light circular resistance bands on the collar of both sides of the barbell and anchor them to the rack. Focus on driving explosively from a dead stop each rep through the entire available range of motion, restabilizing at the bottom position. This will turn up activation and stability that will lead to pain-free shoulders.
By reversing the two phases of the lift, you can help stabilize the most challenging aspect of the movement, which tends to be about 0-3 inches off the chest. This will help you avoid functional pitfalls and blast through sticking points.
As the barbell approaches the chest, many lifters lose upper back tightness, rib cage position, and scapular stability against the bench. This in turn translates into unstable shoulders, which get cranked into unnatural internal rotation and elevation under heavy loads.
This whole scenario can create impingement and increased joint stress on the front side of the shoulders. For heavy pressing, the more stability your upper back can create, the stronger and more fluid your pressing will become.
Though the pin press can be set in a low enough position to have the bar start in contact with the chest, most lifters will be better off training the pin press just above the chest when in an arched and braced position. By setting the pins in a power rack 2-3 inches above the chest, we can limit the terminal end range of motion, making this lift more shoulder friendly while also working through common sticking points.
For lifters with poor lockouts, the pins can of course be raised further away from the chest anywhere within the available range of motion, so position according to your specific needs.
You'll also have powerful starting strength from the dead-stop position. Remember, acceleration is needed to blast through sticking points.