My initial feeling after the first viewing was that Mannix's story was so disconnected from the movie-in-movie bits and other elements dominating the screen time that I just wasn't invested so much in Mannix and his job offer dilemma.
But, all these other characters and scenes getting time on the screen had to have been by design. You don't tie up all this acting and production crew talent with a random pastiche of disconnected vignettes and no story. They've never done that in the past, and there's no reason to think it's happening here.
So, I went back to it and tried to pay attention to the bigger picture, and that experience of the story, for me, was completely amazing. The theme as I read it is one of finding your way amidst confusing, contradictory, or difficult direction, and whether/how we can influence the paths that people take. Practically every character in the story is placed in this situation, and each takes a different path trying to find their way.
Mannix's particular dimension of the story is looking at the question of whether our efforts to control the direction people take is effective. Think about the different problems he's supposed to 'fix' and ask how effective his actions are in fixing them. The answers are wonderfully rich and ambiguous, especially in the resolution of Baird's kidnapping.
The communist dimension of the story is looking at writers fighting for the same kind of thing, but here they want to co-opt Baird and write in communist subtext to help them tell their story from within Capitol Pictures. By the way, since we know there are writers at Capitol Pictures trying to do this, watch the movie again and look for signs of communist subtext appearing in the different pictures.
Each of the movie-in-movie bits present to us Capitol Pictures' view of the world, and each picture depicts a different kind of social issue that masks an underlying contradiction or problem in the real world: religious faith (Hail, Caesar, A Tale of the Christ) female sexuality and purity (Neptune's Daughter), male sexuality and patriotism (The Swingin' Dinghy), and class and intellectualism (Merrily We Dance and Lazy Ol' Moon).
So, I'm seeing it as telling a very broad story, more of a depiction of life for many people, rather than just one day in the life of one guy, and supremely focused on examining the process people go through in finding their way.