Chris- Like you mention, a second capsule would be another way to manipulate the pickup pattern, yet in this case I can't see how another capsule could fit into a standard 406x omni housing with a couple vents on the back side of it.
Jon- Actually I do think of a cardioid as a being a modified figure-8, but I'm a 'basic-principles' mechanical design minded guy. I'm getting off topic here, but an aspect I don't understand is how that modification is physically implemented in real-world microphones to produce directional patterns which are as uniform as possible across a broad frequency range and not just peaking as a bell shaped curve, centered around a single frequency. That's the microphone 'black-art' stuff I guess. All the basic explanations and simplified conceptual illustrations I've come across just show a single pathlength/wavelength arriving at the front of the diaphragm and another arriving at the back of the diaphragm with a phase relationship that varies between the two with source angle, and that seems to me like it would be very frequency specific.
Regardless of how that works in real implementations, I speculate a compelling motivation for a manufacturer to use an omni capsule in a directional microphone design would be manufacturing and production related issues, such as using an already developed and well regarded omni capsule that is in full production, minimizing need for additional capsule fabrication and inventory overhead for a new microphone design. I understand what you are saying on the need to increase the housing diameter to provide a path around the diaphragm inside the housing for a given diaphragm diameter.
Thanks for the 'ah-hah' moment in realizing that the two possibilities I sketched previously are more or less conceptually the same in regards to the path-length phase cancellation/reinforcement. Actually, looking at it again and excluding the interference tube, I realize a pathlength based directional design using an omni element would require an inverted signal relationship between the two paths compared to a typical design. In a design with both sides of the diaphragm exposed to signal, identical path-lengths produce identical pressures on each side of the diaphragm, canceling each other and producing a null. When that interaction happens on one side of the diaphragm only, identical path-lengths instead reinforce one another and produce a maxima. A reverse polarity signal is required to cancel pressure if the two paths meet on the same side of the diaphragm.