If you are attracted to the girl, are interested in her, and want to have sex with her, then it is worth making the effort to pursue her. However, like you are thinking, it's important not too care too much or get too invested in the outcome of your pursual (detachment). It sounds like you got the right idea about not trying "super hard to game her perfectly", and worry too much about every little thing. This is definitely where "needy" game or vibes leaks out, as you are trying too hard, caring too much, and over analyzing every little thing.
I know for me I was a text book example in the past of all these things (pedestaling women, caring too much, over-analyzing, putting out "needy" vibes), overcoming it for me is still a process, but it largely has to do with putting myself out there, and experiencing the rejections, success, flakes, etc., the ups and downs of chasing women. If things work out, cool. If they don't, it's her loss. There are always plenty more fish in the sea.
I know for me I was a text book example in the past of all these things (pedestaling women, caring too much, over-analyzing, putting out "needy" vibes), overcoming it for me is still a process, but it largely has to do with putting myself out there, and experiencing the rejections, success, flakes, etc., the ups and downs of chasing women. If things work out, cool. If they don't, it's her loss. There are always plenty more fish in the sea.