Honestly, I've seen folks try that shoulder lean, but it can make some horses feel trapped and react worse. I like to focus on ground manners first, getting the mare okay with her legs being touched. For instance, I'll pick up the hoof and hold it for just a second, then let go and praise her. Repeating that builds trust so she isn't so jumpy. Sometimes a second person just scratching her neck can keep her mind off her feet. Have you tried breaking the process into smaller steps?

Your garage sounds more organized than my whole house lol.