Doesn't answer your question directly but ..
I found this solution yesterday, and thought I'd try it before buying another new one (my usual solution).
http://www.buttonsandbutterflies.com...-tutorial.html
I have four of the pressing (only) boards.
And I LOVE starch, so they're certainly NOT pretty to look at.
For me, it's less work than attempting to deal with cleaning them.
And very pretty.
Or course, a pillow case would probably work just as well.
For the double sided ones like you're talking about, you could easily attach a of piece hemmed fabric to the pressing side - basting, perhaps?
My double sided one (cut and press) is only the 12"s square, so it's not worth it.