I’ve only rooted two dolls but here is what I did to keep the head still. I used a lap desk that has a hard board on the bottom and a fabric top filled with beans - like a bean bag chair. I turned it upside down. The beans held the head in place quite well, although for a while I used a rice sock to keep it in place too.
The lap desk was put on a pillow(or a few towels) and board part was slick enough so that it wanted to slide around. I then put two of those rubbery things that you use to help get the lids off of jars - they are to improve your grip. Or you could use the drawer liners that are rubbery mesh looking. A wet washcloth may work too - but dry it out each night so it doesn’t mildew. In fact I would use a new clean one each day.
After a while I added a quilted place mat on top so I could wash it to get the stray hairs off.
If you don’t have a desktop like mine I would put some plastic beads or packing peanuts in a pillow case and then you probably won’t need the rubbery things. Of course if you have an old bean bag chair you might be able to either use it or steal some of the ‘beans’. You may need to break up the packing peanuts some.
Below is the desk top the way I write on it - so you can recognize it in the store and the rubbery grip things.