I haven't had the feeling of the phantom hat but I do get the sensation that there's water dripping down the back of my head. I touch my head and there's nothing there. Very strange sensation.
My startle reflex is like yours and you're right, it can be embarrassing. I was having the experience of thinking I saw something in my peripheral vision that wasn't there when I moved my head to look at it straight on. That has mostly gone away for me now.
No advice because I'm new to all of this too but wanted to let you know that someone else is experiencing some of what you are and you're not crazy.