New to your thread, but I wanted to chime in because I can relate to you. I struggle with interaction with others as well. I've always told myself that I am what I am and people will just have to accept that. I'm guessing you tell yourself similar things.
Since GAL is so important you may wish to focus on this area of yourself. Get a library book about self-confidence or social interaction or even the classic How to Win Friends and Influence People.
There are many more people like you than you realize. About half the people you see everyday tend to be introverted and get very nervous or anxious when they meet others. However, just like you they crave contact and connection. Push yourself to be the type of guy that goes right up to someone, says hello and offers to shake their hand. Who would judge you for that? Most people are hoping you do come over and say hello. Then all you need is an initial question. Just develop one to begin with, such as, Do you know if this weather is going to hold up?
Do this to help you GAL not to win back your W, but for motivation think of it this way. If you enter a social situation and are the guy who confidently walks up to someone and says hello and shakes their hand, wouldn't your W find that attractive? Plus this is kind of a 180 for you I'm guessing. Might blow your W away if she catches you doing this.