Okay, so how do I assign these to just the player character and companions? I'm sure there's a way, as I've seen it mentioned before. But how, exactly, is this done?

It is possible. First move the new animations to the file meshes/characters/_male/specanimations, you can name them in order to have multiple versions of the same animation in the same file. Example my character is a samurai so all my animations end with "(sam)" at the end. Just open the CS and the ESP that includes your companion. If you have multiple companions from multiple ESPs then repeat this with each of them. Find your NPC in the Actors area. In the edit menu check the view all button under the preview box. Then select the animations tab. You will see a list of all the animations in the Specanimations folder. Select the ones you want and save. You can do the same thing with the player Actor but if you do it may conflict with other mods, just move it near the bottom of your load order an you will be fine. Then your done.