Hopefully these diagrams clarify what I was thinking. One set of several steel plates is mounted to the bumper plywood with countersunk screws (not shown). The other steel plates hold the magnets, and fit down into vertical slots against one face of the frame rail.
As described above, you don't want the magnets to be obstructed by 0.125 in of aluminum. You want the magnet, directly between two steel plates, making contact with both. The first plate is the backing of the magnet (on the robot), and the second plate is attached to the bumper.
As for magnets, choose something like
this, then pot it in metal-filled epoxy (e.g. Devcon or JB Weld) in the recesses of the magnet backing plate. It has over 19 lb
f per magnet in this configuration. To pull it straight off, you'd need 475 lb
f (likely more than the pullout strength in the wood). To lever it off by pushing at the top edge (e.g. in a robot-to-robot collision), you'd need something like 237 lb
f, not accounting for the resistance offered by the edge of the bumper-mounted steel plates in their slots, or the fact that the opposing robot would be pushing on a rounded pool noodle. If you stand on it, the downward component of the force goes into the slots in the frame, while the magnets pick up the horizontal component.
As for the magnet backing plates, they pull straight up, with a wiggling motion, to remove the bumpers. (Grease their faces to make this easier.)
There's a very rough STEP CAD file attached with details. (No tolerances!)