Here’s Secret Weapon #2… Spray the top of your rubbing plate with a repositionable adhesive. (I call these sprays “Post-it Notes in a Can” because that’s exactly how they work.) Let the adhesive dry for a minute or two and then proceed to make the rubbings.
The adhesive keeps your fabric from sliding around on the rubbing plate. I recommend 404 from Spray and Fix and KK2000 from Sulky. Some of the basting spray products are too gummy, so make sure you test any adhesive before applying it to a bunch of rubbing plates.