I used a PVA glue (polyvinyl adhesive) that is sold as an archival product by a company called Lineco which is a brand of University Products. They make all kinds of stuff for the bookbinding and museum industries all or most of which are considered acrhival. The bottle is sitting on a marble slab I used in a couple places in the project.
This is why I kept the dropout and the orientation - I used it to make the impression in the fabric. I spread the glue and placed the fabric - black felt in this case - over the boards, placed the dropout back in and weighted it down with the marble to dry.
The last pic shows how the mat came out after drying but for some reason looks gray it is black.
I was going to use black velvet and went to the fabric store but the black velvet they had wouldn't work well on this - it was synthetic and they don't have much stretch. A natural fabric usually has a bit of stretch so you can get an effect like this.