Yeah, the pics make a tremendous difference in trying to envision this. I still like the mechanical support idea, but my thought was 90* out of synch with Q's. I was thinking of a flat strap with an axle hole, screwed or bonded to the edge of the panel. Q's angle bracket would definitely be stronger, but I was trying to avoid drilling into the back.
My epoxy approach is somewhat primitive, but I've never been one to prefer form over function. The way that I was thinking of would be to lay the panel face-down on a table and position the axle where you want it on top. Then just slather on the goop, or press it into position if it's solid enough, so that it completely encloses the axle and forms a ramp up to it from both sides of the panel. (Think of a buttress weld, or sticking a drinking straw to a piece of cardboard with chewing gum.) I assume that you want to leave that electronics module accessible, so that would restrict your attachment to the left-most 3/4 or so of the axle. That should still be plenty. I totally agree with Q that adding glass fibre or some other structural material to the epoxy will drastically increase the strength.
If looks are a concern, you can always do some grinding, sanding, and painting after the stuff has cured. I'm not convinced that a counterweight is necessary in this case, since it appears to be well balanced, but such can easily be imbedded in the epoxy on the 'back' side of the axle if needed.