I would like to be able to reverse the stereo channels of the speakers
on my PC through software, i.e. what's currently the left channel will
be right, vice versa. It's not feasible to physically switch around
the speakers!
The sound comes from the motherboard and Device Manager says it is a
"VIA AC'97 Enhanced Audio Controller (WDM).

If you're feeling adventurous and you're handy with a soldering iron,
you could cut off the plug going into the computer and resolder the
wires in the correct orientation. It would not be that difficult to do
(if you're comfortable with that kind of work), but you would probably
void your speakers' warranty.

I was quite surprised to look in the sound & multimedia control panel
and discover (as I'm sure you did) that there is no apparent method
native to Windows XP to swap the stereo.