I figured it out in my case (with the QNAP).
It had nothing to do with the QNAP and the files were not yet in the Trash (deleting from the QNAP is immediately permanent and bypasses the Trash).
Anyway, the underlying cause was that the Finder was locking the files open while trying to "Show icon preview" for certain file types. The result was that some file types would never get locked, because the preview would be quickly and correctly created. Other file types, usually .MKV video files, would get locked while the Finder would attempt to create the preview icon. Eventually, the Finder would stop trying and the file would become unlocked on its own.
So, if I change the View Options for just the folder/share in question and uncheck the "Show icon preview," then they are all immediately deletable from the Finder.
They were always deletable from Terminal using rm.
This would also explain why changing the filename extension would work--it would tell the Finder to use some other program to build the icon preview, and that program, whatever it is, would work faster.