I wonder if a "normal" Left channel would sound identical to the "combined Left channel" in your set up? If the Left channel of your rig sounds identical to the Left channel of a typical rig, then there may be hope for another way. The answer to this (whether or not what comes out of your Right speaker sounds identical in both setups) also has bearing on how big of a difference this technique would make in a live situation in which most of the audience isn't sitting in the sweet spot of the stereo field.
I tried testing the above last night, and I think the combined Left and Right channels are definitely different from, and thicker than, a typical single channel. This suggests a few things: it suggests that the combination would clearly be beneficial in a live context. (Even if part of the audience is only hearing a single side, that side is clearly better.) Sadly, it suggests that there may be no other way to get these benefits. With hope dwindling, I started to move money into different accounts.
It also suggests to me that the benefits may be coming more from the doubling of oscillators than it is from a stereo field. (Maybe describing it that way just makes more sense to me.) It seems to me that if the improvements came merely from it being a stereo image, then we should be able to create this effect by the normal means of creating stereo. In addition to chorus pedal experiments, a slight delay on one side should help get us there. I tried adding some Delay in the Amp Envelope of one layer last night, and, while it puts the two sides more out of phase and gives more of a stereo effect, it's nothing like the combined sounds that S.S. discovered.
The analogy of violins or horns seems appropriate. I've wondered numerous times why DSI isn't making synthesizers with three oscillators. I keep remembering the striking difference that the third oscillator made on my old MiniMoog. I would play one oscillator and think it sounded okay... then add the second and notice how much better it sounded- thinking that it would be a perfectly acceptable sound. But then, when I added the third, it would really put the smile on my face. Still, if adding the extra oscillator was all it took, then we should be able to get these desired results by simply using a layer of the exact same sound, which is not the case. So, S.S.'s technique seems to be a combination of the added oscillators with the stereo field.
So... is there a way to make a patch/layer only come out of one side?? If so, it may provide a way to get this effect for some songs/pieces in a concert without having to change cables and panning at the mixer. I ask because, as Paul noted, there are times when the thickness isn't as necessary in a band context, while other times it would make a big difference (when soloing for example). ...and this option could save me some money.
Regarding the comparisons with other companies, the benefits of this technique don't seem to be a DSI benefit per se. It's not like DSI has noticed these techniques and worked to incorporate them into their instruments. This technique may work just as well with any analog synthesizer. I'm not sure we would get the same benefits with digital/sample based keyboards, but it's worth testing. So far, I've only heard of using this with analog synthesizer sounds. I can say that, when it comes to my experiences with getting analog sounds, this technique provides better and more satisfying results than anything I remember with my other keyboards (e.g. current Yamaha, Nord, Roland, old Korg M1, DX7, Oberheim Matrix 6, etc...)
It does make one wonder what the results would be of linking two MiniMoogs together in a similar way. Or what would happen if we added more oscillators to the '08 combination by panning two complete patchs from two '08's to the Left and another two '08's to the Right? With other instruments, including the human voice, the biggest changes to the tone, when adding other instruments, is found with fewer instruments, with the changes becoming more and more negligible with higher numbers of added instruments.