> Looking at the lobes of the patterns, it almost seems as if the subcard has a smaller lobe than the card pattern.
[reply rewritten] Neumann's Web page for the TLM 170 R has the patterns displayed in an odd sequence, with cardioid stuck in between omni and wide cardioid. If you click them in their real order { omni, wide cardioid, cardioid, hypercardioid, figure-8 }, you can see the pattern become progressively narrower.
> The figure 8, is the narrowest of all. [ ... ]
> If you are saying that the lobes for the figure 8 and standard card are identical, then I get it ...
No, you just said that the figure-8 pattern's front lobe is "the narrowest of all," and you were right! Consider the 1 kHz curves for the front of the microphone. The cardioid's response is down 3 dB at around 65 degrees off axis, and down 6 dB at 90 degrees. A figure-8 pattern, being narrower, has greater attenuation than the cardioid does as you get away from 0 degrees. Its response is down 3 dB already at 45 degrees off axis, and at 90 degrees it has (theoretically) no response at all.
Or think of it this way: The TLM 170's figure-8 pattern is the result of subtracting the output of a backward-facing cardioid from the output of a forward-facing cardioid. (Technically the signals are added, but the rear-facing diaphragm is reverse-polarized so the voltages subtract.) A cardioid still has some response at 90 degrees, so two back-to-back cardioids will both put out signals when sounds arrive at that angle. But due to their opposite polarization, the net result is zero. That creates the null of the figure-8 pattern.
Now, what if you move the sound source slightly forward from the 90-degree null? The output of the front-facing cardioid will increase, while that of the rear-facing cardioid will decrease. The result is an increasing signal of positive polarity. The farther you move toward 0 degrees, the more the front-facing cardioid's output will increase while the rear-facing cardioid's output will decrease. When you reach 0 degrees, the sound source is in the null of the rear-facing cardioid, so nothing much is subtracted from the output of the front-facing cardioid--which is fully on axis at that point.
Move the sound source back to 90 degrees and this time work backwards; you'll get the same progression with the signal polarity reversed. As you approach 180 degrees, the front cardioid puts out less of a signal while the rear cardioid puts out progressively more. But the rear cardioid's signal is being subtracted from the front cardioid's signal--so while the net sensitivity is increasing, the output is inverted in polarity relative to the sound source.
> I am still trying to figure out whether there is some way to isolate the signals from the two figure 8 mics, so that I am only getting what appears to be the smaller, narrower frontal lobes of the figure 8, and canceling out the rears.
The answer to that is still no. What makes the figure-8's front lobe narrow is the subtracting of signals of the rear-facing cardioid within your TLM 170. If you cancel that rear lobe, you also cancel its narrowing effect on the front lobe--and then you've got yourself a cardioid all over again.
Whether you do this with an M/S matrix or a mixing board with a polarity switch or in any other way, that's what you'll get. I'm sorry; it's pretty much a 2 + 2 kind of thing, and you're going for 2 - (-2) as a variation, but it still adds up to 4.
--best regards
P.S.: I was out walking and thinking about your initial question; I have the feeling that we're still not quite addressing it. I think this may be because your point of reference is a Sony stereo microphone with three cardioid capsules, one of which points forward (the "M" signal) and the other two of which are used to synthesize a sideways-facing figure-8 (the "S" signal). Maybe you didn't realize that the signals from the two side-facing elements are combined in opposite polarity--not simply added or mixed together. And maybe you wanted to subtract the signals of those left- and right-facing elements from the "M" microphone so as to narrow the front pickup pattern of "M".
The signals of the left- and right-facing elements aren't available separately--but if they were (as with some quad microphones having a "clover-leaf" pattern of cardioid elements, e.g. the Neumann QM 69 from the 1970s), this would indeed narrow the front pattern of the "M" microphone. At the same time, however, the overlap between the two side-facing elements (centering precisely behind "M") would create a rear lobe in opposite polarity to "M"'s front lobe. So again, it's the same result as what you get by simply dialing in the hyper- or supercardioid pattern of your TLM 170, or very nearly so.