For EC, I think it's best if you had a friend's friend who is a girl, and you can practice maintaining eye contact from there. It just takes a lot of practice really, you can actually practice to anyone at all, even guys or whoever.
I noticed you mentioned "people you feel above you". Thing is you should never feel that way. You should always feel that everyone else is actually on your level, or you're a step higher. Otherwise you'll only demonstrate low value, and it's very unattractive.
I too actually had the same problem. But I guess what helped me was that I always remembered that phrase, "The eye is the window to the soul". And from that, by means of communication, you want to capture people's souls. But honestly I guess it's not really about being shy or once shy. It's more about having a good social etiquette.
So yeah, just keep practicing and remember to look in the eye when you're actually talking to the person, or any other person. It'll soon be more like a thing you have to always remember to do like floss your teeth