Steve,
> This one corner seems like an ideal location for some floor-to-ceiling corner bass traps. But should this type of treatment be symetrical around the room? <
Bass trapping works best when it's spread evenly around the room. It doesn't have to be perfectly symmetrical in the sense that a control room needs to be symmetrical for proper imaging. But if you treat only one corner the low frequency waves will bounce around a bit before they find their way to that corner.
There's a good explanation of corner trapping in the Acoustics FAQ, second in the list on my Articles page:
www.ethanwiner.com/articles.html
There's additional information and suggested placement drawings on my company's site:
www.realtraps.com
--Ethan