In the past when we have used this type of insulation foam board we have glued muslin (cotton fabric) to each side of it.  Since often the warping in this or even wood happens when you get one side wet, if you glue to both sides it kind of "warps" evenly so you end up with no warping.  Don't know how much sense that well make to folks but it works.  Also the muslin cover gives the foam more durability.  The same principals should hold true for the velvet.  Actually you could use the velvet on one side then a cheaper material on the other side.

Shawn what kind of glue did you use? I've been experimenting with spray adhesive, wallpaper paste, elmers I'm not sure what I want to use. The spray adhesive I bought is "foam friendly" but, you can peel off the material rather easily. I've got to find the right adhesive.

I was thinking that perhaps a light framework attached on the back would help, but now I'm curious about the muslin. It does sound like it would help with the warping in an odd kind of way.

Elmers or really any brand of white glue.  You can actually water it down some if you want. Five gallon jugs of white glue where a main stay in the theater design shop I worked in.   You are right that spray adhesive kind of just lets you peel it off, although this can sometimes be helped if you spray both surfaces and let them set for a few minutes then press the two together.

I thought I would add while we are on the subject of this type of foam and construction with it, that we once built a large waterfall wall that was carved out of huge blocks of styro foam. Since it was a waterfall and needed to use real water we took it to a shop that does spray in truck beds. (http://www.rhinolinings.com/) We had them spray the entire thing in green then once we got it back we added color detail ourselves. It made for a very durable piece of scenery. While it may not be feasible to do this for smaller projects, I am pretty sure that the product they use is similar to the spray on tool dip you can get in hardware stores. You would need to test to make sure it did not eat away the foam though.

Funny you should mention that. I happen to have a gallon of truck bed liner paint lying around. I may try that out on a scrap piece just to see how it reacts.

How funny! 

Well, after some experimenting with the elmers and with spray adhesive I've decided spray adhesive is definitely the way to go. The elmers glue takes too long to dry and soaked through in spots. The spray worked best but the fumes were friggin horrendous! Definitely do this in a well ventilated area! Oh and cover stuff up because everything will be sticky!