Landmine presses are an effective "middle of the road" exercise between overhead work and true horizontal pressing exercises.
If you really think about the arm path, this isn't much different than an incline press, so why does the incline press cause people more shoulder problems than landmine work? It has to do with the fact that having the upper back pinned against a bench limits the ability of the shoulder blades to freely rotate upward – they get stuck down into scapular downward rotation.
I like the idea of starting with a carry because it teaches you where an appropriate "finish" position is, and then you can work backwards from it.
If you've successfully completed overhead carries, you can go to a one-arm bottoms-up kettlebell military press. The bottoms-up setup is more shoulder friendly because the unstable environment shifts more of the muscular contribution to joint stability than actual force production. This is great if you're rehabbing a bad shoulder.