Must a flush-mount panel actually be flush?
This is where it does get a little hard to follow things in the NEC so here we go. NEC Article 408 covers Panelboards Part 408.2 is about other articles that apply to panelboards. 

So from there we go to NEC 314.20 which covers boxes and a panel is also a junction box. That a flush box must not be set back more than 1/4" from the surface and that's only if the material is non-flammable. 

You might try and see if you can find some one who can fabricate a metal extender since I don't think anyone makes one for a panel. The extender would have to be between the exposed wall and slide in external to the panel and secured in such a manner as not to interfere with the panel itself.

You might also check with your AHJ and see if he would grant you an exception but I don't think they would go for it since they are fairly conservative in their thinking.

Sorry for the bad news, good luck.