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.com/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.