My Mystic is overweight as well, she does her best but does not always manage to clean herself properly.

This will sound like it is mean, but I DO NOT HURT her by doing this.

I use my left hand to grip her face and then cradle her head close to my stomach/chest area. With my right hand I either comb her back area of if she is a little messy, I take a warm face cloth and clean her. She of course does not like to be handled like that but it is the only way I can handle her by myself and get her cleaned at the same time.

I would keep trying to keep her combed...she may get used to you doing it and will maybe tolerate you cleaning her after a while.