@JonB My EDIT revision now prints the column heading I wanted. Hopefully I only need to run that header saveState function just before program exit, and restoreState just before displaying my table on the next run. If that does what I want, I won't need to directly deal with "visual indexes" at all at this stage in my ongoing "personal movie database" project.
Once I can persistently re-sequence columns, I hope to add several more columns, with the less interesting ones dragged to the right of the row out of the way. I already remember user-revised column widths, so I can make those rightmost columns as narrow as possible, but I fully expect to progress to optionally hiding temporarily unwanted columns.
Anyway, I'm getting older and slower, so it'll probably take me a few days just to implement "moved column memory" in my app. But eventually I want several members of a "cinema club" each having read/write access to their own database (on DropBox, GoogleDrive, whatever), and read-only access to the other members' databases (to retrieve "rating" and "date seen" values by user).