Can a non-Jew participate in any of these shul honors?
- opening / closing the ark
- carrying the Torah to / from the bimah
- hagbah (lifting the Torah) and / or gelilah (wrapping the Torah)
- reciting / leading the singing of the ending prayer songs such as "Adon Olam" / "Yigdal"
- gabbai (to distribute aliyot and other honors to other congregants and / or as one of those next to the Torah reader to correct possible mistakes)
The commonality in most of the above is that they do not involve the recital of congregational prayers. Adon Olam / Ygdal are at the end of the service, and from what I understand, supplements that are not considered the main part of Musaf.