I tried becoming more "socially adept" for quite a while, but even though I can put on a pretty lively appearance on the outside, it's just not me. I'm an introvert and I accept that.
One of the best bits of advice I've heard recently is to "focus on strengths, not weaknesses." That is, there's no point hammering away improving at things you're bad at, and ending up mediocre at everything, if you can focus on the things you already kick ass at and become world class!
Most people who are socially inept tend only to be so with the public or people who are not considered close to them. Take Stanley Kubrick. He got a reputation for being an appallingly bad socializer, yet most of his closest contacts talk about what a friendly and amazing person he was.
So.. enough people are socially awkward, or even downright grating, but are or were world class in their field. These people should be an inspiration. Don't hammer away at making yourself a socially popular person if it takes energy away from being kickass.. because if you're kickass, you don't need many social skills.