Slumber sledding. I like that.
Try putting silicone sealant or if silicone doesn’t stick, Shoe Goo, on the bottom of your sleeping pad. Either one will create friction against silicone impregnated nylon. However, if your pad won’t take either glue, put silicone sealant on the ground sheet. The best silicone I’ve found for this is Duco’s Automotive and Marine 100% Silicone Sealant and Glue. It is less likely to rub off than McNett’s Silnet. Sil sealant works with silpreg groundsheets. Barge’s cement works on Tyvek. I don’t know of anything that sticks reliably to plastic sheeting.
One thing: If you don’t stake the groundsheet down, it may slide on the ground, obviating your efforts to increase friction between the pad and the groundsheet. You can use parachute cord to tie the groundsheet to the tie-outs on your tarp. For simple Tyvek or plastic groundsheets, just tie a sheet bend in the up-hill corners of the sheet.