The eyeknots that I have seen in pictures you had published, are NOT Helical loops ! 
They do have helical turns on the Standing Part, but the two ends of the helical coil are not the direct continuations of the Standing End and of the on-going eye leg… In the Helical Loops, it is the single and the double nipping loop of the common and the double bowline that have been replaced - and they were replaced with this “open” helix, a nipping structure where no point is in contact with any other point.( In a “classic” bowline, there is one such point, the “crossing point”, in the crossing-knot-based PET eyeknots, there are two. In a Helical loop, there is none ! )
I know that one can not easily imagine that an “open” helical loop can be as secure as a “closed” loop - but it is ! Myself, I have discovered this during the discussions we had about a mid-span bend (1), when I was trying to figure out how one could attach a second line on a tensioned main line - and just after that, I had realized that the same most effective friction mechanism could be utilized in eyeknots. After I had tied and tried some of them, I had discovered that this idea, of the multiplication of the friction when the ““first curves”” are multiplied, was already widely known ( as one might had anticipated, of course ), and already applied in climbing and sailing. See the picture of a mooring shock absorber ( “snubber” ), based on such a coil. Here the purpose and function are slightly different, but the principle of an elongated “Standing Part”, so its contact area with a compressible “core” is more extended, remains the same. I have seen similar mechanisms in climbing equipment.
