Idk, i feel like standing shoulder press requires the core to be engaged too, to an even greater extent at that. Granted, the Z press takes your legs out of the equation, but it somehow feels more stable.
Basically if i had to put the exercises in a ranking
(less stable, more core engagement)
Standing shoulder press
Z press
shoulder press on bench
(can use more weight)
Like most exercises, I think it really just comes down to the individual. I agree with your ranking, but clearly
@Johnny Salami had the opposite experience.
For example, I can't feel my chest for shit when doing a standard bench. I need to go wide or decline to really feel it where I need to.
So ultimately, imo, it comes down to trial and error. If someone feels their core engaging more doing a standing Military Press, do that. If they feel it more in a Z press, do that instead.
I'd also argue that, in the end, using compounds to feel specific muscle groups is pointless. If someone wanted to work on ankle mobility you wouldn't recommend squats, right? You'd tell them to do Calf Raises and stretch more.
So if
@Tsar Nicky is wanting to work on shoulder mobility/flexibility, stretching and yoga would probably be better than lifting alone would be. Because having strong shoulders doesn't mean shit if you can't move em. As for lifts, maybe some lat/front raises and some sort of wide Grip row/rear delt work. You're presumably using every head of your shoulder when pitching, so you'd want to work every head.
But that's all based on my own experience so, grain of salt and whatnot.
Edit: Hell even V Pushups would be a good thing to add into the routine.