Finally found what I've been looking for!
Pill Free Double Knit Crescent Cover 5 Pack
In my 12 years as an LMT, I've bought so many face cradle covers that were described as "soft" or "smooth" and found that most weren't. So I only ordered one 5-pack of these to see how they are. Well, they're supersoft and smooth! And they fit real well over a face cradle with a thick fleece cover on it.
The only unknown is how long the elastic will hold up with a lot of laundering, but time will tell on that. I'll be ordering more real soon!