I found this demonstration showing how to mount panels spaced off the wall (or door) using 4" metal post base brackets, on the Real Traps site: http://realtraps.com/mini_door.htm
I was able to find the brackets in local hardware stores by searching for "post anchor".
Your panel would need some kind of cross-braces on the backs, to give it a lip/ledge to hang against the post base.
Another way I've seen Ethan spacing panels is by using a spacer behind them (similar to what it sounds like you've done), but then, instead of attaching the panel with screws through the spacer, he used picture frame wire to attach the top of the panel to the wall, letting it hang such that its own weight holds it against the spacer, and holds the spacer in place against the wall. Then he secured the bottom of the panel with additional wires. This method is quick and dirty, but not as rigid. http://realtraps.com/placing_mt.htm
Hope this is helpful,