Looking better with each revision. I am not CAD proficient yet, so all I can do is kibitz for now. Your original idea of aluminum "U" channel into the backboard was not a bad idea. If the channel is straight and a good fit to the thickness of the board (epoxy?), and can be attached so that it is backed up by the strength of the board and made parallel in the opening, it would resist the forces of the cantilever without flexing. That could be accomplished with 2 half backboards that were tied together top and bottom after the metal channels are attached.
The carriage itself needs to have a rigid member between the left-top and right-bottom bearings so that it does not flex and tilt the bed. Perhaps the missing middle piece of the backboard...
I bet that Nicholas could have helped more with this if he were not away right now.