I'm always a bit suspicious when people use putatives like 'believe' in assessing and improving certain conditions.
Get a correct diagnosis.
You can't the a complete OH press delts-only. The traps will always come into play, somehow. As will your levatores scapulae. And some of those muscles attach to the neck.
Have you tried 2. from my previous post?
Damaged sterno-clavicular joint. Dito ac-joint.
I've built my delts and traps mainly using the BTN press. I got a decent shoulder girdle from that.
After a few forced lay-offs and not being able to do any serious OH pressing for quite some time and doing a few radical diets, it's no wonder I had lost deltoid size.
Got that in check by doing ISOs, whereas lateral raise variations (machine, standing, seated, standing and leaning away etc.) play a big role. Also a combination of lateral and front raises. And lots of upper back work. My shoulders are just growing off this.
By the by: the stuff I've outlined uses high volume and medium to heavy weights, but not super-heavy resistance. Super sets, 8x8 and stuff like that. I'm using that for my delts.
Intensity is the key, here.
Actually, I've never had a muscle group react so kindly to this approach. The amount of blood resulting from this pump might even have helped the healing process, there (I'm getting prolotherapy).
DBs are usually better for shoulder health, but the aforementioned contraindications (trap involvement) still apply, here.