Very interesting thread, and kudos to you for making yourself uncomfortable on a regular basis. I think this process is key to personal growth, though it sucks a lot when you're going through it. Keep at it.
Personally, I am an introvert who can be socially adept, in the right crowd. Generally I dislike crowds of any kind; I love a quiet night out (or in) with a few people I know. But if I am obliged to spend time in a crowd, I try quickly to pick out one or two people to get to know and focus on them. Social settings where I really suffer (e.g. withdraw, get up and leave, etc) are the ones where groups are set on making inside jokes, making fun of everyone, assuming everyone is the same and not actually getting to know individuals, etc. I hate those kinds of settings and I don't even try to be socially adept there.
That said, I wanted to comment on the introducing question. I always try hard to introduce whomever I'm with, since I don't want them feeling left out of the conversation. The only time I do not introduce someone is if the exchange is very quick (Hi, good to see you, bye), in passing... then I don't see the worth in introducing, since there won't be time for a conversation anyway.
If I am the stranger to the situation and my host does not introduce me within, say, 3-5 minutes of the conversation's beginning, at the first pause I will stick out my hand and say a bit non-chalantly, "Sorry, I didn't get your name..." then get their name, and say, "Okay, cool, nice to meet you. I'm abaya." At that point, usually my host will realize what a cad he/she has been, and apologize for not introducing us. Everyong chuckles a bit and the conversation moves on.
Let us know how it goes for you...