Cut each page into equal parts - the scanned-spread fix
Yes - that is exactly what it is for. Choose "side-by-side parts" and 2 parts, and every sheet becomes two pages in reading order.
Each part reclaims that many millimetres from its neighbour, so a word sitting right on the cut appears on both parts instead of being sliced in half. Leave it at 0 for a clean margin between columns.
Yes. The cut is made on the page as you see it, with the rotation applied, so "side-by-side" always means side by side on screen - not in the underlying page coordinates, where a rotated scan would be cut along the wrong axis.
Yes. Each part is clipped to its own region rather than being a full page pushed off the edge, so the text of the other half is not left hidden inside the file.