Do you think it would be possible and within the framework of halacha to tie the tzitzit according to Rambam (similar to the Teimani community), however without using the Yemenite knot, but by using a method similar to the Chabad way of separating the chulyot. I’ve included pics to show you. Thank you for your time and info.
Halachically, your method certainly fulfills the d’oraita requirements of kesher elyon and one chulya of 3 winds.
As for d’rabannan, however, Rava (Men. 38b) requires a knot on every chulya, and though not everyone paskin’s like Rava, the Rambam does as he explains in Hil. Tzitzit 1:7 – wherein he says to “make a knot” at every chulya. And Tosafot seems to make of this requirement a knot on every set of chulyot (one white and one blue). The Radzyner explains that the sheeta of the Gra incorporates the knot requirement to be exactly 5 such that one would make a knot on ever white,blue,white,blue combo.
Now the Radzyner believed that the knotting requirement is for the traditional 5 knots (See Ptil Tekhelet, 1313-133), and he also maintained the need for the 13 hulyot which could be accomplished by simple looping (like in your picture). Furthermore, there is an explanation of Rava’s requirement for a knot on every chulya which states that the knots are needed in order that one can visually distinguish each chulya (See R. Y. Rock, https://www.tekhelet.net/pdf/rak.pdf). Now, though your picture does seem to fulfill this need to see each chulya, I wonder if such chulyot will not eventually all bunch together since they are not held by a tight knot. Also, though you use the Radzyner loops for chulyot, you do not have the 5 knots that he would require.
In conclusion, though your tie is biblically “kosher”, it does not fulfill various Rabbinic requirements, and I am not sure what advantage there is to using it. Let me be clear here: If you use all blue wraps then you should be able to see each chulya by having space between them (otherwise you should have intervening white chulyot which would provide the needed distinction). And even if you say that the Radzyner’s chulyot are not any more distinguishable, nevertheless he has 5 knots which according to his calculations based on the Zohar and other writings is sufficient.
– Mois Navon.