In my opinion its developing confidence in yourself. Developing confidence in yourself and in your ability to succeed and perform in social situations such as this.
I believe we struggle in situations like this simply because we lack confidence in ourselves. i.e. around people you are comfortable and calm around and have confidence that you will perform and cope you have confidence that you will perform well. Yet those people we are not comfortable and confident around we struggle badly. We go into these situations knowing we will struggle to cope and perform.
Its this subconscious belief of what we are is what causes the problems in my opinion. i.e. we know accurately how we will do, and when we know we are going to fail - that is basically what will happen. We need to change that value we have placed on our beliefs to rise as high as possible so that we go in believing we are going to succeed.
I also believe we place a subconscious value on ourselves in comparison to others. When we value someone very highly and of course we value ourselves lowly, that huge gulf in inferiority and inadequacy causes huge problems on confidence. i.e. you don't believe you are good enough, you focus on your perceived flaws and being inadequate, you feel self conscious, you feel negatively on yourself and that anxiety is what causes the problems speaking and thinking and being your normal self.
i.e. that is why I believe people are so anxious around people they fancy, no matter if they have SA. Because the person you fancy you have placed a very high value on them, and unless you think extremely highly of yourself then you will have feelings of inadequacy, maybe not good enough for that person, lacking confidence around that person, etc.
It also explains why you feel more confident around people you see as equals, but why we feel anxious around authority - as you place a high value on them compared to yourself if you are lacking confidence and do not have a high status. It also explains why people get all anxious around celebreties and people they idolise.
I believe the answer is to increase the value you place on having the ability to succeed, perform and cope in tasks/situations and to have a higher opinion in ourselves - believing we are good enough, concentrating on how cool we are and how much we have to offer - and then the gap in the values we place on ourselves in comparison to those we are anxious around lowers - giving us confidence. Same as with the situations - increasing your value on you ability to succeed, cope and perform lowers the gap between your own ability and the value you believe you need to succeed, cope and perform in a situation.
Therefore developing confidence in yourself, increasing self esteem, self worth, self belief, belief in your abilities to do the tasks is what the solution is.
In my opinion anyway. I know others will disagree.