Completely stripped 4mm recessed allen key bolt.

Whelp, this is extremely frustrating. I've got a completely stripped 4mm hex screw, completely recessed in the frame. This is a proprietary sort of seatpost design where there's a wedge mechanism that sits inside the seat tube of the frame and when tightened, expands and wedges the seatpost against the frame and wedge itself, similar to the giant defy or giant propel.

This screw is recessed inside the frame at about a 30 degree angle to the frame. Any ideas how I can get this out before I start drilling into this with a smaller than 4mm drill bit like a maniac in the hopes of drilling right through the screw? I cannot dremel or cut at this as it'll cut right into the frame. Supergluing an allen key method is too risky too as the glue can easily spill out and go around the inside of the wedge.