Reach tall at the top and don’t worry about keeping the shoulders packed down and back.
Allow the elbows to rotate and point outward at the top of the movement but tuck them tight to the ribcage at the bottom.
Fight to control the bar from rolling your wrists into extension and think about “rolling your knuckles toward the ceiling.”
Keep momentum out of the movement and don’t add any additional leg drive by flexing and extending the knees.
Squeeze your glutes and brace your abs as you press. You shouldn’t be leaning back excessively as you press.
Imagine you’re trying to look out a window at the top, your ears should be in line with your biceps.
If your shoulders are bothering you during the movement, consider experimenting with a wider grip or utilizing some of the vertical pressing progressions listed on the site.
You can use a staggered stance to prevent the lower back from arching excessively but if you still can’t control the anterior core then consider using a half kneeling regression shown on the site.