The "aperiodic" enclosure is an oddity, and there must be a reason why no one else thought it worth duplicating. The reason that no one else thought it worth duplicating is that it didn't do anything other than lower the Q for an enclosure that wasn't as big as it needed to be for the woofer. This sort of emulated a larger enclosure, taming the big response peak that would otherwise have been conspicuous, somewhere in the mid-bass. The tradeoff was that bass also leaked through the opening and cancelled with the front-radiating bass. The net effect was an overall reduction in bass which was stronger in effect at the mid-bass hump than elsewhere. There was no Helmholtz radiator effect, i.e., there was none of the familiar effect of a ported speaker. It is also worth noting that the use of damping material in the opening did not do anything different from simply making the opening smaller. To say it plainly, it was a kludgy design that didn't really make good sense.
I was a fan of Advent back in the day. I first heard the OLA speaker in the early '70s. It made a memorable impression on me because it was apparent that it was a good deal less colored than even good speakers from that era generally sounded. Sometime in the early '80s I walked into a hifi store one day and saw that they had a bunch of the last large Advent that was made before Jenson bought them. This supply of Advent speakers had evidently been liquidated by some distributor who wanted to get them out of the way, and the retailer had bought a big stack of them. I recall that I bought the pair for about what just one of them ordinarily sold for.
The big Advent woofer was unusual in several respects but was a much better woofer than Jensen's cheap commodity woofer. It may not be widely understood that in order to get deep bass from a woofer in a sealed enclosure the driver Q actually needs to be rather high (in relation to Fs), and that this was achieved by using a magnet that wasn't very strong such that the electrical part of the damping was weak. One of the downsides to this is that the suspension stiffness (the spring effect not to be co-mingled with damping) has to be unusually low, lest the enclosure will end up being inconveniently large.
In the last large Advent speaker that was produced prior to the Jensen takeover, Advent engineers had already switched from the "fried egg" paper tweeter to a true dome tweeter. By the early '80s it was no longer necessary for Advent to manufacture their own custom paper tweeter in order to have a tweeter that they deemed superior to the small cone tweeters that were common in the '60s and '70s. Kloss' fried egg tweeter wasn't ever a great tweeter. It might have been better than most cone tweeters from the early '70s, but not even this is certain. It sounded different, and many people liked it and some still do, but the obvious question is whether this may have been due in major part to low-order harmonic distortion. I suspect so.
Once I had that pair of big Advents in my possession, it was probably only a matter of an hour or two before I realized that while they sounded pretty good, they didn't compare favorably to any number of better speakers that were then available. They continued to hold their own in terms of value. I doubt if there was anything else you could buy in 1980 that sounded quite as good and that didn't cost a lot more. At one point I paired them up with a pair of EPI-100s, wired in parallel of course. This combination actually did sound pretty good, for a while anyway. The dullness of the Advents was made up for by the brightness of the EPI with that inverted dome tweeter, and the excessive brightness of the EPI was made up for by the stronger bass of the Advent. I quickly grew tired of the mismatched look and eventually decided that the EPI colored the sound so much that the Advent sounded better by itself notwithstanding the dullness. I occasionally contemplated ways to improve the Advent, but it would have been a lot of work that I didn't think would have been worth doing unless it was converted to a 3-way, and at that time I would have expected to encounter difficulty with the crossover design. I would have ended up with a Frankenstein speaker that would only serve as a constant reminder that I had expended a lot of effort on something that would have made other people ask why I didn't just buy some new speakers. I kept the Advents for a period of time vastly greater than I would have imagined when I bought them. Roughly twenty-five years. Sometimes I wish that I had not sold them, but the way this kind of thing works is that if you still own them you are wanting to sell them. All in all a pretty good speaker and a great value speaker, but not a great speaker when value isn't a strong consideration.
The double Advent thing was also curious and never really made sense, for reasons that are well understand by anyone who has ever dabbled in speaker design. The pair of tweeters are further apart than the operating wavelength at even the low end of the tweeter range. As soon as you get a little bit vertically away from the horizontal plane passing between the two speakers, you start getting interference/cancellation, and the familiar comb filtering effect applies in upper treble if you are as little as a foot or so above or below that horizontal plane (unless you are very far away from the speakers). In fact the vertical separation between the two woofers, together with the fact that the crossover point was fairly high, meant that the same thing occurred in the upper part of the woofer operating range. The only true benefit was the improvement in bass, which was significant and which would have included pushing the F3 point a little bit lower. There can be little question that the enhanced emphasis in bass was the reason that people liked this arrangement. A better result would have been obtained by stacking them without inverting the upper one and with the tweeter disconnected in the lower one and with a simple modification to the low-pass filter in the lower woofer to limit the upper end of its range to some very low frequency, below the frequency where the mid-bass peak was found (which was due to the moderately high Q and which accounted for the "warm" sound that was widely appreciated). The lower woofer would then be essentially a passive, sealed subwoofer without much deep bass extension, but beneficial nonetheless. This would be better than the stacked arrangement that was a very peculiar fad back then, but would still be a kludge that wouldn't make much sense unless maybe you already had a spare pair of big Advents sitting in a closet and otherwise not being put to good use.