I haven't tested anything, but there are these changes:
24.0.68 (12/10/2018)
13. Fixed: Non-imported files were not moved with selected media files even if "Move all files..." checkbox was checked on "Rename, Move, & Copy" dialog window, when the action was initiated in Explorer view.
14. Changed: Moving files with "Move all files in folder (including non-imported files)" checkbox checked will only skip moving files that are at "main database location".
15. Changed: "Move all files in folder (including non-imported files)" checkbox on "Rename, Move, & Copy" dialog window is renamed "Move all non-imported files in folder with selected media files".
That would be why the Wiki says one thing, and MC does something else. The Wiki is out of date. You have imported these extra files, so they won't be moved unless you specifically select them.
I think you need to unstack the files you want to move, select them all, and then move them. You will need to make sure that the file naming doesn't cause an issue. I would expect that the name is changed, but the extension isn't.
I would have to set up files and experiment to work out the best solution. Not today!
You could try just doing a move, without a rename, for all stack members. i.e. Just change the directory, not the filename.
You could try removing the extra files from the MC Library so that they are moved using the setting above, then use the MC "Extras" functionality to view the files. But that may not be appropriate if you have lots of image files in a directory which associated extra files for each of them, as all extra files would be moved when just one, or all, file are moved.
You could make a more complex expression that did file renaming based on the file type, in addition to tags.
Maybe provide some more information, confirm you have imported the PSDs, JPGs, etc., someone can make better suggestions.