I also use a best friend grazing muzzle on my easy keeper. You need to adjust the muzzle so that there is only about a 0.5 to 1 inch space between the nose and the bottom of the muzzle, this reduces the muzzle moving up and down too much.
Also, I find that I have to do some "creative" placement of fleece to keep it from rubbing a lot. I bought the halter tubes and just cut them and place them were they need to be.
My guy was rubbing under his chin and this seemed to fix it. Good luck.