Thank you but my question still stands. Perhaps it is the case that the css class table.moduletable is only generated when a list (table?) of audio tracks is involved, whereas my testing involves a single audio track. I'm not saying this is the case, but it might explain why I'm not seeing that class, and why neither it nor my module class suffix is visible in the page HTML source. The player module does have a Joomla ID, and that number (of 3 digits) is used to generate an html element ID named <div id='jwplayer###'> where ### is the Joomla ID.
As I mentioned, my question is based on experience with other Joomla modules, and in the course of that experience I have read and re-read multiple times the Joomla documentation on this topic - so I think I have a reasonable grasp of what is supposed to happen here.