I wonder if this could be done with something like the mechanism used in expanding anchors. Slide the tool into the hole, turn a screw to expand the end, and then back out as the reverse countersink is cut. Then turn the screw the other way to collapse the cutter and retract the tool. Not a lot of room for the mechanism.

As long as we are cutting AL, it could be made from mild steel. Beyond that, use oil or water hardened drill rod.

Rick