Interesting that Jome figured this out about the tongue. I have just downloaded your document to read over later, but I was in the process of preparing a thorough on the topic with such additions as you mention here. I as well found that control of the tongue is essentially not required for the piston action in the airspace, and actually was naturally doing a cheek piston action for the longest time when equalizing at depth. However, this would not allow me to perform a very long or effective equalization on a mouthfill. I then realized I was using the cheek instead of the so-called "tongue". Adjusting my operations I was suddenly able to equalize to max depth and extremely comfortably. I once again assumed I was doing the frenzel-fattah technique as described because it was working now. As I began exploring other aspects of equalization and was paying close attention to details, I realized it was not even the tongue or the cheeks that I was using as the main source of piston action. It is the jaw. Dropping the jaw down, the cheeks pull in, the tongue lies flat, and air fills the space. Then closing the epiglottis and resisting bulging at the cheeks with the cheek muscles (easier than the attempt to piston with the cheeks), one closes the jaw. This is the main source of force for myself and other long time practitioners of the mouthfill.
So, I as well was going to elaborate on this, since it simplifies greatly the process of learning and deploying the other parts of the frenzel-fattah technique and achieves great equalizing results.
For interest to this thread as well, I have always naturally equalized since starting to freedive, and always assumed I had the ability to valsalva and frenzel. Recently I think I have discovered that I do not have the ability to perform valsalva or frenzel without adding my instinctive tendency to perform BTV. I can put huge pressure into my nose without performing BTV and this does not force open my eustacian tubes. The same with Frenzel. I found this out while studying the nature of BTV using my natural tendency in comparison to a friend's (currently) inability. The results as well I hope to publish soon. This all is pointing towards a potential conclusion that many people may have eustacian tubes that would require much more pressure than they would generate through valsalva or frenzel, yet most of us with this as a potential problem, access a degree of BTV in the process which loosens up the eustacian tubes. Anyhow, for now I just wanted to let all those out there know that even a person with natural and easy equalization technique, seems to have the inability to perform valsalva or frenzel equalizing, without the aid of voluntary control of the eustacian tubes. My suggestion for these people is to stop fighting and learn to control the tubes. If you keep in touch I will have lots of info on techniques to assist in this process.
Cheers,
Tyler