How can I organize album on iPhone Music App by artist and album artist in iTunes on Mac?

I think I know the answer but am going crazy trying to find it answered precisely in the community.

I want my iPhone music from iTunes sorted such that (1) the “Artist” view groups all songs by the song artist, and (2) the “Album” view groups the music into albums by Album Artist. However, for compilation albums, when I set the Album Artist as the individual artist for that track, the album is split up in the Album view, and when I set the Album Artist as the album name or some other indicator, the Artist view uses that Album Artist identifier rather than the song artist. Turning the Compilation flag on and off does nothing to get the arrangement I want, nor does the Sorting field on iTunes. Am I right that I am just out of luck and will have to live with album names who are not real artists living in my Artist view forever?

Any help/confirmation appreciated!

[Re-Titled by Moderator]