I'm also confused a bit by the 'bedspread'. It sounds like you are actually making a whole cloth quilt out of home dec fabric?
Are you using batting?
First of all, why aren't you using muslin (or wide cotton backing) on the back? You said the top fabric is slippery and you are using something similar on the back. I think it would slide right off the bed. If you are not using batting, a cotton fabric would go a long way to stabilize the project.
As the other posters said, please give us a bit more info.
Sounds like an interesting project!!