The "Poyis" for the Kohen

The Mishna in Yuma discusses the Payis and the Talmud expands upon it in great length primarily in the second perek. Interesting to note what the relevance of the procedure on how to appoint specific Kohanim for specific jobs is to the talmud. For example, we don't discuss who/how the technical procedure of making the ktores is all we know is that Bais Avtinus makes it. An interesting question is asked by the Shaagas Arye (both in the sefer Shaagas Arye and in Gvuras Ari on Yum) why is the kohen allowed to wear or actually obligated to wear the arba'a begadim during the Payis if according to the Rambam it is Kilayim and Assur to wear "shelo besha'as avodah". There is a discussion that the Payis can be halacha l'emoshe misinai and not just a mitzva derabanan. I would take it a step further and suggest, based on the Shaagas Aryeh, that the Payis might be considered part of the avodah more than just a "hechser" for the avoda.