Congratulations on conquering your fear of spiders! I agree with Copper that SAD is much more complicated than other specific phobias. The key difference I can think of is that other peoples' thoughts/feelings/actions are involved in our SA - it's not that we are afraid of people as an 'object', but we are afraid of the things they will think about us, say about us, do to us etc. Given that (most) people have brains, it's quite hard to predict what others will do, and impossible to know what they are thinking about us. This means that it is much harder to lose the fear of social situations, as we often can't be sure that our fears aren't actually true.
But, having said all that, no doubt it can be beaten. You've made a good start, just keep at it!