My current thoughts:
1. Put a collar on a drill bit to limit the depth to, say, 3/8". Allowing for the drill point, that should stop about 1/16" short of the outter surface. However, any little slip-up could spell disaster.
2. Get a length of 1/2" square hardwood stock and and glue it to the inside surface. Clamping would be difficult, but perhaps I could use some short screws to hold it in place while the glue dries.
Which would be best? Any thing I've missed?