I'm kind of apprehensive about magnets living in an earthquake prone zone so I'll probably end with some kind of hook system going through the rivets or the holes. so that should allow the knives to be mounted closer the back.
My idea was to get a wall mounted jewelry display ordered of etsy, which is basically what you have there. Then, I would finagle some sort of hock attachment system. my concern in planning is making sure it kind of still looks like picture frame instead of a wall mounted cabinet. But I would love 3 display panels that would close shut.