The four types of thread 3 wool and one linen comprise the Eifod. This would work according to the opinion that the Avnet was shaatnez. However if it was not shaatnez, how was this Eifod made and how would the limeade work?
Sholem, UK
I think that when the Gemara states that "Danim MaiAvnet" this refers to the Avnet of all the year round; not the Avnet of the Cohen Gadol on Yom Kipur. All 4 of the White Clothes of the Cohen Gadol on Yom Kipur, including the Avnet, were of Pishtan alone, but the Limud here is from the Avnet of all year round.
The source that the 4 white clothes of Yom Kipur, including the Avnet, were of Pishtan alone, is from Yoma 35b; that the work of the day was in "Bigdei Bootz"; and Rambam Hilchos Klei Hamikdash 8:3. Teshuvas Radbaz [Lileshonos HaRambam #1470(97)] writes that the Avnet of the Cohen Gadol on Yom Kipur did not contain Shaatnez. However the Gemara 71b "Danim MaiAvnet" is referring to the Avnet used all year round, which was of Shhatnez.
KOL TUV
Dovid Bloom