@@bernixix, actually I did get it working, but I'm not quite sure which step fixed it. I will try to explain my setup for the benefit of others who run into this.
I am running Rocksmith on my home-built PC with an ASUS P8Z68-V LE motherboard, utilizing the on-board Realtek audio and running Windows 8.1. I have been through many guides to get this working, but at this point Audio Exclusivity is enabled in the game and the .ini files are all back to default settings (I believe).
The first thing I did differently this time around was to set Bandicam to run in Windows 8 Compatibility Mode. This was really a shot in the dark, but I really didn't have much left to try! I had noticed some guides reference the setting Win 7 (WASAPI) but mine said Vista (WASAPI), so that sent me down the Compatibility Mode path.
After that I went back into the Windows Sound Settings and I found the Stereo Mix device. It was disabled so I enabled it and made it the default device on the Recording tab. I have been through guides that utilize this device, but I *swear* it wasn't there before. Perhaps it showed up when I was updating every driver I could find and I didn't see it until now?
I set it as the Primary Sound Device in Bandicam.
And voila! I have sound.
https://www.youtube.com/watch?v=U1cjyDqhlU8&list=UU_t2KaVAqlz6n1cSq7xwnHg
Obviously I need to work on both the lighting and that solo, but hey, at least I can quit messing with it and get back to playing now!