Techelet Tzitzit Tying Options

We get a lot of inquiries regarding techelet tzitzit. Yesterday we received the following question from a prospective customer at Tulane University:

I am interested in getting tekhelet on a tallis. Under tzit tzit tying customs I see Ashkenazic and Raavad among others. I was under the impression there is no general Ashkenazic tying custom for tekhelet. Is that only for non tekhelet tzit tzit? Thank you. 

He's right. There is no consensus on how Ashkenazim should tie techelet. But the standard Ashkenazi option as you know it is not recommended, because it was formulated in the absence of techelet, and does not meet the Gemara's stipulations for tying tzitzit with techelet. We only offer it as an option for those who insist.

Rambam - Many Sephardim choose this, because the Rambam is a major halachic authority, especially for Sephardim, and just about all of the other tying methods were proposed by Ashkenazi poskim. Sometimes Ashkenazim go with the Rambam as well.

Arizal - The default option for Chassidim. This is essentially the same as how Chabad ties their all-white tzitzit. It probably looks the most similar to the standard Ashkenazi tying custom

Sefer HaChinuch - Rabbi Eliyahu Tavgar, the rav of the Ptil Tekhelet Association, recommends this as a default option for Ashkenazim.

Vilna Gaon - This is probably the most common choice among Ashkenazim, presumably because the Gra is considered such a significant halachic authority.

Raavad - Sorry, I don't know much about this custom. Some would say it's the closest to standard Ashkenazi because it has 7-8-11-13. So it's like Arizal, but without linking the wrappings into chulyot.

These various techelet tying customs can be seen in action on this page.