I feel your pain as it is something that used to effect me on a daily basis when I was first starting out.
The way I got passed this was nothing to do with changing my structure or "game", but instead changing my relationship to "game" and getting girls.
The entire PUA industry is built on the foundation of men desperately needing to fix this part of their lives. It is understandable, as having attractive women in your life as a man is an essential and natural need. So, with this being stated, the whole process of getting better, interacting with and seducing women is taken SO FUCKING SERIOUSLY!
Guys make pick up(yes, even "natural game") so god damn clinical, that any element of fun and enjoyment is sucked out of it due to the self placed pressure. It becomes a means to an end which most guys will spend their lives chasing the monkey on their back, never getting there.
My biggest realization....was to stop taking any of this too seriously. Stop placing seriousness on any one conversation or girl. Stop going in with a desired outcome you must impressively manouvre yourself towards with stealth like perfection, because that shit does not exist.
Now when I interact with girls, it is only to test the vibe, to see if we can have some chemistry. Yes i am attracted to her, but thats all I am feeling. I do not give myself a goal to complete or even to close. Closing happens, only if I enjoy her and I want to see her again or sleep with her.
I never go in to pick up or seduce...only to charm. To have a charming, playful, and flirty interaction, with zero negative pressure on me OR the girl. Negative pressure is created by the pressure you place on yourself before you even get to her. Women feel it, and they want to get away from it.
Have you ever been around a really uncomortable guy or girl, it feels awkward as balls, and you want to get away....this is what the majority of pick-up creates in its students.
Your only job(in my experience and eyes), is to be polarizing, and simply show up, progressing only when you feel the desire to.
Have fun, but not in a needy clown way.
Keep it light, and the huge approach numbers will decrease substantially. I know this to be true as I have been coaching men for the previous few years full time in this exact area.
Best of luck mate!