So no measurement comparing monopoles (sealed) dipoles (panels and bass reflex) and cardioid below schroeder?
This is an interesting question. Intuitively it seems like radiation pattern wouldn't make much difference in the modal frequencies; the waves are still vastly larger than the space.
The advantages of cardioid alignment in outdoor and large space PA systems don't apply to domestic spaces.
Ferekidis and Kempe investigate and compare the low-frequency mode coupling in small rooms of monopoles, dipoles, and cardioids in in this paper:
https://www.aes.org/e-lib/browse.cfm?elib=12663
The figures mostly speak for themselves, but the cardioid manages to couple as well as the dipole and monopole regardless of room position (e.g. where the dipole couples poorly and the monopole couples, well, it behaves similarly to the monopole and vice versa). They also note the benefit of being able to rotate the cardioid speaker for controlling the mode excitation (e.g. by pointing the cardioid null in the direction of an intrusive mode). This can also be used to strongly reduce front-wall SBIR, particularly if the speaker is pulled out from the wall far enough that the first dip occurs where a conventional speaker is omnidirectional (or close to it).
One of my speakers, the Gradient revolution, has a dipole bass section that can rotate independently of the top part of the speaker, this way you can direct the dipole nulls in such a way that a mode is minimally (or maximally) excited.
Overall I agree with Geddes that the room is the main determining factor for low-frequency reproduction (and that the natural solution is multi-sub), but this does not mean that the loudspeaker doesn't matter (as Ferekidis and Kempe show). The room modes will still be the same, regardless of speaker, but how they are excited depends on the source(s). None may sound "right", but some may be closer to "right", and some may give the listener a greater flexibility in adjusting the speaker to the room.