You show that the “Chabad” tying method is the same as the “Radyner” method however the Baal HaTanya says to use 2 strings of blue and 2 strings of white (like Tosfot) wheras the Radzner says to use one half string of blue (like the Rambam). Can you please explain?
Referring to the relevant seifim in the Shulchan Aruch Harav (see https://www.tekhelet.net/diagrams/ChabadTyingSource.htm), you are correct that the Baal Hatanya holds that the strings should be according to the opinion of Tosafot. Nevertheless, his explanation of tying appears to be like the Radzyner – though he only writes “leave some distance” to make the chulyot visible – this of course would be impossible without some kind of wrapping to hold the demarcation. Thus the method of tying adopted by Chabad is to use the shamash to wrap around the various chulyot as the Radzner suggests.
– Mois Navon