Success! Finally realized why HDRI wasn't working for me. I remember seeing a short while back a tutorial on lights for Vue by Silverblade. Well, turns out I was creating my HDRI map incorrectly, and should have been saving the file as a HDR image, rather than a JPG.
Like, Duh!
Loaded that image in back into the scene, and what a huge difference it made. More light, better shadows!
This image was done in this fashion, with no other lights.
...Insert some witty or thought provoking comment
here...