I've read your post about 10 times now and am still trying to wrap my little brain around it.
I'm trying to wrap my head around this, too. Simply having control of how much rear-facing Mid to add would only allow one to, well...add reverberant sound. So I assume in decoding double MS it's possible to
subtract the rear-facing Mid from both the forward-facing Mid and Side. So in double MS, the ratio of the rear-facing Mid to the front-facing Mid and Side (and whether one's adding/subtracting it to/from the other signals) control the reverberant sound, while the ratio of the front-facing Mid to Side controls the stereo width.
The attached image generated with the Schoeps Double MS plug-in may help. It's a two-dimensional representation of the mics and patterns in play:
orange = forward-facing cardioid Mid;
yellow = figure-8 Side;
green = rear-facing cardioid Mid. If my assumption above is correct, and you're able to visualize it from the image, you may see how subtracting the rear-facing cardioid would significantly reduce the reverberant sound.
Hopefully DSatz will chime in with further clarification. Neat stuff!