So this might not be accessible to most lifters but I found it to be an interesting way to train the overhead press. This was motivated by a minor shoulder injury I developed doing pull-overs (fuck them).
If you have access to a cambered bar (shown below), load it up with a normal weight you would press. Get the cambered portion facing upward to so the barbell makes a "concave down" shape. Grab the edges of the cambered portion so your palms are somewhat facing eachother and clean it to your chest (this can be difficult). Then rotate the bar 90 degress so you are in the pressing position similar to a log, the weight should be offcenter from your grip. Now press! youll find this takes a lot of stress of the rotator cuff but adds a grip and core component.
Cambered Barbell Example