Gutbucket, your statement:
> [ ... ] most cardioids get more omnish at the bottom so a stereo pair would have more mid and less difference in the stereo signal down there.
... doesn't generally apply to single-diaphragm cardioids, which can very well maintain their directional pattern down to the lowest frequencies in their range. The difference in effect is considerable, both for M/S and X/Y stereo recording, since the listener's sense of spaciousness is closely tied to the difference in low-frequency energy between channels (more specifically, to low correlation between the two channels at low frequencies). Dual-diaphragm cardioids are basically wide cardioids at low frequencies, so the low-frequency pickup of a stereo pair of them tends to be very nearly mono.
Incidentally (or not), this phenomenon is probably responsible for the mistaken impression that large microphones have better bass than small microphones. Nearly every large-diaphragm microphone ever made has had a dual-diaphragm capsule. A large dual-diaphragm "cardioid" microphone will pick up low-frequency sound energy from all directions in a room, while its pattern will become narrower than a true cardioid at high frequencies. See the attached polar diagram for a microphone based on a dual-diaphragm capsule design which has been very important in the history of recording. Along with that I've attached the polar diagram for a good single-diaphragm cardioid from the same manufacturer, which remains a cardioid all the way down. Similar examples could be shown with microphones from other manufacturers.
--best regards
P.S.: With regard to Alan Blumlein's "phase shuffler," you have to realize that Blumlein mostly didn't use what is now called the "Blumlein" stereo recording method, and didn't do so at all in the beginning. One of his patents describes the method in principle, and many years later the method of using crossed figure-8s was named in his honor. But as I recall no figure-8 microphones were available to him at the time of his early stereo recording experiments (though they certainly existed), so he devised the phase shuffler to help emulate their effect with near-coincident omni (!) microphones. I'll try to dig up some references.