I also highly, highly recommend checking the growth factor shoulder training article here by CT. The first complex (muscle snatch, snatch grip BTN press, clean grip BTN press, Bradford press, savickas press, push press) sets the entirety of my shoulders on fire. I do it at the end of press days. Seriously, I have to use body English to swing my arm up and grab my jug off plazma off the shelf after 3 rounds of it with just the bar.
I also get that when I do EMOM press, absolutely roasts my shoulders and definitely not just the front delts.
I have never felt anything from lateral raises aside from the traps and weird feelings in my shoulder. But that's just me! My right shoulder has nerve damage and Lat raises just feel really awful with it, but it definitely grows from aforementioned barbell movements