Hi, Doltologist. I completely sympathize with you on the eye contact thing. I don't think one-on-one eye contact is difficult at all, but in my work as a teacher, teaching content while focusing on the eyes and behavior of a class full of students is very difficult for me. And, if you don't manage to keep your eyes on the students, they become disengaged and you can lose control of the class as far as classroom management is concerned.
Also, when I'm concentrating on teaching, I forget to smile. Also bad for keeping the class focused.
My biggest nemesis is the Job Interview. With a half dozen pair of eyes looking at me, I forget everything I've ever known about teaching. I'm sure I score abysmally which is likely why I still haven't found a permanent teaching job.
I definitely have difficulties with eye contact and body language monitoring, too when dealing with groups of people. I feel you. I definitely like people, but I just can't take too many at a time.