So a line underneath the shaded section worked very well (added with Foxit Reader similar to the instructions on
this page). Running k2pdfopt with the
-col 4 option then correctly interpreted the page. See attachments I checked the algorithm for the column detection, and it doesn't presently have an option where a large vertical gap between regions (see attached "gap_example") would be a signal to treat them each as an individual set of columns. That might be something to consider for a future version.