I was going to say; this sounds extremely E1. Then I read through to see that's what you've settled on for now. I am inclined to agree with this assessment, and the 9-wing. I also very strongly relate to what you said here (though as I get older it becomes less and less important); a huge drive to be perfectly self aware on an objective external level.
1's have a lot of stereotypes that can lead to folks not typing as them, in particular if the individual does not see themselves as a broad perfectionist or having a strong desire for "order". The thing is, it can be focused only in certain areas and still be apt for the person. You definitely do strive for accuracy from what I can tell, and you want things to be "just right", 5's can be like that as well but there is a differentiating factor between them. A primary 5 wants to learn for the sake of learning, and will go about it however it needs to be. 1's aren't entirely like that.
Another thing that can shy some folks away from 1's (which I believe applies to you), is honesty. It's commonly says that 1's are extremely honest with a strict moral code that is not deviated from. To lie, cheat, manipulate is thought to be a huge violation and wouldn't ever be attempted. That's simply not true. It's true, their moral codes are very often quite strict and they won't bend from them, but this wrongly assumes that all 1's moral codes are "clean and pure". Even then, 1's can absolutely go around their "moral rules", all that needs to be in place is that the ends justify the means. While this doesn't manifest in all type 1's, some of them are like this (I am one of them). I am fully honest and self-disclosing 90% of the time, and everyone around me in my life regards and reveres me for being so... because that's exactly how I need it to be so I can abuse this when times call for it. It's all in the name of getting things "right". At the end of the day, I can be profoundly manipulative.