I have a pair of APM-22ES speakers that are configured like the one's on TVK, with square drivers for both woofer and tweeter.
http://www.thevintageknob.org/SONY/sonyes/APM22ES/APM22ES.html
As you can see on TVK, only three models of the 22ES are referenced - the ES, the ESB (black), and the ESV which used ferrite plugs to magnetically shield the speakers for use close to a television, so I am curious to see your II's.
The only references I can find to an APM-22ESII on the web are either in french or german so perhaps it was a model only sold in the EU.
Is it possible that the tweeters were replaced at some point? The crossover point between woofer and tweeter is pretty low because of an issue with the woofers. A 1986 Gramophone review put it this way:
"In the present case, for example, its behaviour is reasonably good up to about 2kHz. At just over 3kHz most of the radiation is taking place from the central area and but little from the outer edge, indicating that the flat plate is saucering, i.e. alternating between convex and concave. In order to minimize acoustical irregularities from this cause, it is desirable to cross over to a smaller unit quite early, giving the designer of a two unit system the difficult task of producing a tweeter which will reach down to meet it, and still behave well up to the highest audible frequencies."
I have an original service manual for the 22ES which gives the crossover frequency at 2KHZ but TVK states it at 1.3KHZ. In any event, it is pretty low giving the tweeter a lot of work to do and as a result, I have read that they were prone to failure. So possibly the original tweeters in your 22ES's got fried and were replaced with conventional drivers.
Another possibility comes from the service manual which, for the AEK, UK models (Made in W. Germany) lists two different part numbers for the tweeter as follows:
8-927-177-00 (Black)
8-927-197-00 (Walnut, Ebony)
The second part number (197) matches the one for the other model listed as the E Model (Made in Japan) in the manual and matches the part number on a loose spare driver that I have so it is definitely for the square tweeter. Check one of your tweeters to see if it might match the other number.
That's about all the help I can be for now. I have pictures I took of the crossover in one of my 22ES's as well as some shots of the back of the woofers showing the rather odd construction and how the VC is connected to the diaphram. If anyone is interested I can either post them on this thread or start a new one.