Your first clue is push on terminals, found on the 14 woofer, the 15 has the same red/black button spring terminals as most Altecs through the 70's used.
Also note in your post #25 the clear EIA and date code. 391 is Altec, date code is 13th week of 1981, spot on for a model 14/9842 monitor.
"Actually, according to Bill at GPA (who can re-cone these) the stock 34633 woofer for the Model 14 does have a 3 inch voice coil (he and Todd both speak very highly of this woofer) whereas the stock 33785 woofer for the Model 15 (which uses the same woofer as the Model 8 and 9) does not. The 34633 is a significant upgrade over it's predecessor, the 33785.....
Interesting, since this is exactly the information i've been trying to drive home since my first post. I have been well aware of these facts for several years, and Bill is not always spot on with his information, hence the AKer that claims Bill told him a 413 ia a 12 inch woofer.
Now, for the ESS woofer. I've been holding the baggage on this one. But, that frame looks EXACTLY like the woofer frames from my AMT towers, EXCEPT, my woofer frames were stamped steel. However, the shape of the basket down to very small details is extremely similar.
A google image search for "ESS woofer" fetched this:
This is what my ESS tower woofer frames looked like, so not as similar as i recall, but still a very similar overall aspect: