One small mystery solved.
A lucky break came my way, and I found the right sharpener at a local bookstore – a place with no other International Arrivals products that I could see.
Much larger than just a general large hole sharpener, with slots specifically sized for their two pencils, the product brings some resolution to the problem.
The oversize fluorescent pencils are made usable again – and the carpenter’s pencil is pointed. Of course, this point is like that of a regular pencil, and discards the lead’s rectangular shape. Who wants carpenter pencils pointed this way? I suppose it beats nothing.