okay so I was in the same boat the other day with the whole non slip thing and this is what I have done. And it works great. I found this product at walmart I cut it and put it inside the clip with linning glue and wow my dd played in it all night after we got home and it never had to be replaced. I was worried it may fall out and a child could put it in thier mouth and since the reason for looking in to the whole non slip was for a little baby I'm going to let my dd play with it for a few more days b4 I make one for my friends baby. sorry for the book but I thought I would share.
Here is the product YouTube - Non.Slip-Pad
Or something close to it.