Your situation is definitely peculiar. Have you tried looking at the audio path, or DSP studio's analyzer, or at your audio device's monitoring utility to see if any sound is being played on any channels when this is happening? I guess I'm wondering if the channels that the DVD is playing on aren't channels that are mapped differently in your setup? It is unusual to see a stereo DVD, but not unheard of (concert DVDs will sometimes be in stereo).
Your normal 12 channel setting will not do downmixing for you (it has a 7.1 mixing target) so if anything the normal 12 channel setting will upmix the stereo DVD to 7.1 if JRSS mixing is enabled, which would obviously be undesirable. However, 2 channel in a 7.1 container should do the downmixing just fine (assuming you've enabled JRSS mixing). I use 2 channel in a 7.1 container regularly.
So I guess my advice is: confirm what is happening during playback in Audio path (# of channels, mixing, potentially forgotten DSP settings, etc.), then have a look at analyzer and see if sound is playing back on an unexpected channel(s), and then have a look at your audio device's monitoring panel and see if any audio is being sent anywhere.
The fact that it works with a standard setup suggests there's an issue somewhere in the mixing chain; you may have a few channels muted somewhere in your DSP chain; you can diagnose that by selectively disabling a block and seeing what happens). I've never encountered your issue, but all of my video is 5.1 or 7.1 so there may be some special challenges with 2 channel video that I'm not aware of (i.e. maybe it's not mapped to L and R or something crazy like that). If these steps don't help, I'd suggest posting your DSP studio settings (screencaps)