Changing my mentality toward the physical and emotional response that I experience prior to an approach is a HUGE part of my success in overcoming approach discomfort. Another pickup author (Eric Disco) talked about how somebody running a mile for the first time is going to be experiencing considerable physical discomfort that, with experience, becomes part of the exhilaration of running.
I would like, however, to take a moment to share some personal experience. Having suffered from time to time from REAL anxiety, as you've defined it, I might have some insight. (To qualify this claim, there were times in college when I locked myself in my dorm room for days at a time and even more recently that I've remained alone and hungry in my apartment because I didn't want to face an encounter with people at the grocery store or the pizza delivery guy.)
Approach discomfort is a component of real social anxiety. When you DO have to go out in public, you're not only afraid of approaching others, but you're actually afraid that others might try to approach you.
Generally, I agree with what you're saying about thinking about your experience using language that helps you to cope with it more effectively. Part of the therapy that I've gone through to overcome my own anxiety is a technique called Rational Emotive Behavioural Therapy (REBT.) I wanted to offer a germane counterpoint though, since there are genuine cases of approach anxiety manifested as part of a larger social anxiety disorder. There are probably one or two people reading this site that have a real problem and I'd like to make sure that they don't feel marginalized, but rather that they feel encouraged.
This and pretty much all broad scoped theories, methodologies or anything to do with pickup, are aimed at people in general and not people with severe mental problems. I know quite well the difference between the two things I've described because I get anxiety attacks similar to what you mentioned getting and I know that they are extremely debilitating. Approach "discomfort", as you called it, on the other hand (which is actually what Jsmooth and myself were originally talking about introducing as a concept to the community, but which I still felt didn't aptly describe it) is NOT anxiety, it is merely discomfort over that feeling of excitement.