I recently made a chenille wall hanging from a panel. The directions I found said to add the binding before washing. I would think that if you left enough backing and batting around the panel for the width of borders you want to add, Then sew the chenille strips and cut; then add the borders, you'd be fine. Although I'm not sure about the squaring up if necessary.
You could go ahead and make the chenille part, square it up and then do some variation of QAYG to add more batting, backing and borders...? Just brainstorming here.
Mine turned out great. What panel are you working with?