The Lexicon SL1 seems the best tool for directivity research as it solves the challenge you mention.
"Ulrich said that the narrow radiation control extends to below 80Hz":
www.lexicon.com
Here is a picture showing Dr. Horbach with the SL1:
FollgoTT clued me in to the work of D.B. Keele and Ulrich Horbach, who wrote some papers on how to control directivity of a loudspeaker using a combination of driver spacing and FIR filters...
www.diyaudio.com
With regard to research vs. development, I still vote for the former when it comes to SL1.
Below linked presentation documents part of the research that finally led to the SL1.
It describes vertical directivity control and dates back to 2007. From there it's still a big step to the SL1.
I absolutely agree that the SL-1 is a successful design - for its purpose - at least what I was able to hear of it 20 years ago. I knew Ulrich and Don Keele well.
As for research into the effect of loudspeaker directivity, if you have read my book, especially the 4th edition, there is much discussion of what is required to convey the perceptions of being in a large space with an orchestra - the concert hall being the definitive reference. The goal is to deliver to a listener's ears the sounds that would have arrived at the real venue - or - to deliver the perceptually most important sounds, because it turns out that a diffuse sound field is not a requirement for our perceptual systems. It is an interesting exercise, leading quickly to two conclusions on my part.
First: binaural recordings reproduced through headphones with head tracking are best. Crosstalk cancelled loudspeakers reproducing binaural can be a viable option, with some setup constraints. (Section 3.3 in the 4th edition)
Second: loudspeaker reproduction in small rooms requires multiple channels - more than two - probably 5 for concert hall envelopment and 7 for movies requiring persuasive flyovers. (Section 7.2 in the 4th edition). Atmos offers a vertical dimension, mostly useful for sound effects in blockbuster movies. I have been in demonstrations where one could walk around much of the listening room without losing the soundstage and the sense of being "there" in a concert hall. Stereo doesn't make the cut.
But stereo is the default standard, so enthusiasts have sought other ways to expand the soundstage and improve envelopment, the most common is multidirectional loudspeakers - bounce sound off the walls. There are omni, dipole and bipolar designs, and simple arrays spraying sounds in multiple directions, including the controversial Bose 901. Some have designed specifically asymmetrical dispersion patterns that combine a more active somewhat omni sound field with steering of the principal lobe to attempt a bit of time-intensity trading to stabilize the soundstage to entertain multiple listeners (Section 4.3.3 in the 4th edition). It was a mixed blessing, but had a following. Compared to the SL-1 it was a very simple array (it was many years ago), but the SL-1 addresses only a single off centre listener, a different objective. I suspect one could do better with modern technology, but time-intensity trading is a problematic concept when dealing with complex musical sounds.
The real-world problem with any multidirectional loudspeaker is that it depends on the room boundaries to deliver the off-axis sounds. All rooms are different, and most are not as spacious as the ones used to demo the true benefits of such designs. Having the ability to vary the directivity is a convenience, albeit an expensive one.
From the psychoacoustic perspective, multichannel audio is the easy winner - even tasteful upmixing is beneficial for many stereo recordings. All that has been historically missing is a recorded repertoire, but it is significant and growing. Fortunately all movies and most music videos have multichannel sound tracks. When I have visited music and sound recording schools the demonstrations have mostly been multichannel - sometimes many, many channels. Interestingly, gaming employs binaural methods and I have been told that this might be where the "action" is. I am not a gamer. The challenge for the marketplace has been the cost of multiple loudspeakers, and for many people sound quality was compromised. Now, with the advent of meaningful measurements and competent designers, timbrally neutral loudspeakers are available in affordable packages. Without neutral loudspeakers multichannel systems function poorly - the loudspeakers draw attention to themselves. Done well, it is impressive.
In the end one puts one's money where the perceptual rewards are. I have had multichannel audio since 1988, starting with the Lexicon CP-1 (Consumer Product-1). from the mind of another brilliant engineer, Dr. David Griesinger, who also, years later created what has been to me the best stereo upmixer I have experienced (Lexicon Logic 7). As I describe in the 3rd edition, at the time I had built the largest "concert hall" I could afford as our living/dining room (7800 cu ft) and energized it with a pair of almost omni Mirage M1 bipole loudspeakers. It was very entertaining, but really needed more channels (Section 7.4.6 in the 3rd edition). My multichannel system in the home theater was then showing promise and was much more versatile. I have not looked back.
So, as has been said, there are "horses for courses". Set your personal target and there are ways to approach it.