I second the recommendation for a full strainer inside the back of the frame. I'd consider pocket screws to attach it. Look up Kreg jig if you're unfamiliar.
A cleat, either z-bar or wooden, would be appropriate to hang it. With a little preplanning, you can build a strainer that is angled inside to act as a cleat that meshes with a complimentary angled wood cleat mounted to the wall. As long as the outer frame is reasonably secure, you should be fine.
James