I'm not sure why it is square, but that hole is actually how the draft hole was drilled - at some point inside the shank, the two holes merge. Think about the geometry - drill bits are straight...
Pipnet, oyster knife, senior reamer, and a triangular machinists scraper is what I use along with a set of chip carving chisels to clean up an "estate " meer - followed by sandpaper on a sharpie.
I run a 5/32" aircraft (that simply means long) bit through the shank on all my meers and a 1/8" through the 2-piece mortise / tenon adaptor - that gives me the perfect draw...
I use a set of chip-carving chisels to persuade the carbon away from the meer... Just remember, it's not a race - too little is better than too much...
You might want to hold of on the Jojoba oil until the repairs are complete... The Jojoba oil could interfere with whatever adhesives you might need to use.