"Has anyone heard of The Tannoy Method used for speaker toe in?"
I have not heard that name before.
"The speakers are toed in quite a bit past the listening axis."
I have been making speakers intended to work well with this sort of configuration for about fifteen years.
"Is there a benefit?"
The short answer is, there are at least three benefits when done right: Less coloration, deeper soundstage, and wider sweet spot. There is one possible detriment: The soundstage may not be as wide. And, the technique probably will not work well with most speakers.
Warning, the long answer gets a bit geeky and technical. Please skip if that sort of thing doesn’t appeal to you (I post this because my sometimes geeky posts have offended people).
First a bit of background on relevant speaker design, which probably applies to the Tannoys: Imo the kind of speakers you want for this are ones with a fairly narrow and uniform radiation pattern over much of the spectrum. For example, you could use a 90 degree pattern (-6 dB at 45 degrees off-axis) constant-directivity horn crossed over to a large diameter midwoofer at the frequency the midwoofer’s pattern has narrowed to 90 degrees. Tannoy’s concentrics probably have similar radiation patterns, with the midwoofer cone acting as a constant-directivity horn.
Next, a bit of background on the effects of early sidewall reflections: Early reflections are more likely to cause coloration and degrade clarity than later ones, and strong early same-side-wall reflections play a role telling the ear you are in a small room which tends to overlay the soundstage on the recording, and in particular soundstage depth. Strong early same-side reflections do however broaden the soundstage’s apparent width, albeit at the expense of some image specificity, because the early sidewall reflection is smearing the image widths a little. (Personally I prefer to just move the speakers a bit further apart.)
Finally, a bit of background on how the ear localizes sound: The ear uses two mechanisms to localize sound: arrival time, and intensity. With a normal speaker setup (mild toe-in), when you are in the center sweet spot, the arrival times and intensities are the same from both speakers. If you move your listening chair to one side, the near speaker naturally "wins" arrival time, but it also "wins" intensity, because you are now on-axis (or nearly so) of the near speaker but you have moved further off-axis of the far speaker. So the image tends to shift towards the near speaker even further than your chair has shifted.
Now imagine speakers having the proper radiation pattern and 45 degrees of toe-in, such that their axes criss-cross in front of the listening area. For the listener off to one side, the near speaker naturally "wins" arrival time, but the far speaker "wins" intensity! This is because you are now on-axis (or nearly so) of the far speaker but well off-axis of the near speaker. These two localization mechanisms offset one another somewhat such that you still get a decent soundstage, though of course imaging is best up and down the centerline. The key is, the output of that near speaker must fall off smoothly and rapidly as you move off-axis. Relatively few speakers meet this criterion... most speakers have a pattern that is too wide and changes too much with frequency for this technique to give good results.
This well-controlled radiation pattern combined with the extreme toe-in essentially eliminates the early same-side-wall reflection. In fact the first significant sidewall reflection for the left speaker will be the long, across-the-room bounce off the right side wall, and vice-versa. So the first significant lateral reflections arrive at the opposite ear from the first-arrival sound, and this relatively late-onset cross-correlated reflection is generally interpreted by the ear/brain system as spaciousness rather than coloration and image widening. And thus with less small-room signature superimposed atop the soundstage on the recording, we hear more of the recording and less of the room.
I wouldn’t say the technique "takes the room out of the equation", but imo it does usefully reduce detrimental room effects. At an audio show where we used this sort of setup, an electronics manufacturer who was sharing the room with us for the first time remarked that it was the first show where they were not "fighting the room the whole time". (We were doing something unorthodox in the bass region as well, which is beyond the scope of this thread.)
Duke