Well, given that confusing dialogue where poor Joey implies that Spock's his boss (the "you don't rank me and you don't have pointed ears" line to Sulu) as well as the fact that he went with Spock to pick up a scientific party and that Spock seemed to know him very well, I always figured he was a scientist of some sort.
Your "non-greasy" jobs observation hits closer to the mark for me now that you've explained further, but Rand and even Uhura arguably had those sorts of jobs, too, and wore red. Janice actually almost perfectly fits what you described. So I'll agree to disagree with your group's analysis. I think if I had watched in production or airdate order originally (I didn't; I don' t remember for sure, but I'm *almost* positive that I first saw S3 episodes as a kid), I would have concluded that blueshirts were the scientists and the redshirts were the catchall group. By S3, that was more obvious.
For sure. We were having the discussion late last year (so, the analog of late '66) and stuff wasn't set in stone. Indeed, Uhura, had worn gold three times, which suggested communications was originally "line". Admittedly, security and yeomans seemed odd as red, but the engineers clearly weren't "staff" so... (also, we just got Marla McGivers in red, which makes no damned sense since last I heard, anthropology was a science!)