Ralph, I think it comes down to what I relayed Bud being adamant about - a backloaded horn (BLH) and true TL are the converse of one another.
I believe your seminal work was done with a pair of Frieds, yes? The Frieds couple magically with the Atma Spheres. Even the current four ohm versions. In fact, the low impedance does not at all present the expected difficulty you see in more typical loudspeaker offerings. Bud was never surprised at this, and chalked it up to his raison d'etre - the resistive, not reactive loudspeaker via true TL, low Qts drivers, and (most importantly) series crossovers.
Unfortunately, as you know, he passed away (wow, has it really been almost a decade?!?) before I could really get it all out of him, and though he did provide a thorough and well thought out and worded explanation at the time, I'm unable to recall enough to discuss it intelligently. In summary, more or less, the TL will taper down as one moves through the line, snuffing out the backwave. The BLH will do the opposite, expand, and amplifying it. The ramifications of this are not subtle.
Fast forward a couple of years...a friend of mine who you know pretty well began using a well-known pair of single driver BLHs. One day we tried several tube amplifiers on them: an 16 wpc 211 SET, 15 wpc 300B PSE, 78 wpc Class A push-pull tube, and an 60(?) wpc OTL (not Atma Sphere).
For whatever reason, the first two amplifiers were head and shoulders better with these speakers than the latter. A real surprise, as other more ubiquitous speakers we had tried in the past always yielded the expected results. The two triode amps came across sounding powerful, particularly, the 211 SET. Most surprising, the 78 wpc PP tube amp, which one reviewer claimed sounded like 150 wpc, just could NOT put power into the speaker. Very strange, indeed. The OTL was thin, harsh, and lacking its typical low end performance. Perhaps, it could handle the driver itself, but the folded horn presented something far more difficult for it to push through.
Along these lines, I do believe there is something there in terms of the impedance these speakers present to an amplifier that is much different than the norm. It might not be something folks have yet been able to measure or quantify, but it's something that can be felt, heard, and experienced.
My own Hornings have been a challenge, the biggest I've had to work through in audio. Several times, I came close to giving up on them. The one thing that remained in my mind to the contrary was that Jeff Catalano has always done a masterful job in setting them up and producing what I consider perhaps the most natural and beguiling sound of any room at a show. It's taken me several years to get to the point where I now believe I can have these (or the next iteration) for the long term. Of course, no speaker (or product) is perfect. I do wish they imaged a whole lot better than they do. But the combination of clarity, dynamics, overall realism, and that aforementioned naturalness is something I do not hear in most loudspeakers I've been around.