You sound a lot like me, and I am ILE. I fit with every one of those words you used to describe both LII and ILE.

I still haven't really found an entirely satisfactory description of the E vs. I dichotomy, save for that it alters the function orientation. While it is true that extroverted types tend to be outgoing and social and introverted types tend to be withdrawn and antisocial, it is not necessarily true. It goes both ways. Personally, I identify more strongly with INTp when going by the dichotomies but the functions just weren't right. (Ne-Ti and Ni-Te are very different and it shouldn't be too difficult to determine which is closer to you if you are considering these two types). I even identified as INTp with the Reinin dichotomies (which I later came to find was due entirely to misunderstanding of a few of them).

If you know that you use Ti-Ne as your ego functions, then it shouldn't be too hard to determine whether you are LII or ILE. LII's, being Ti dominant, primarily create logical systems and methodologies. ILE's, being Ne dominant, primarily consider potential or possibilities of an idea or situation. From the way you described yourself, you definitely seem more irrational, and you pretty much nailed Fi PoLR exactly.

Then there are the Reinin dichotomies... like MegaDoomer said, I don't think the Reinin dichotomies or subtypes are intended to be definitive, but they are useful tools.

Just for reference, what LII and ILE Reinin dichotomies do you disagree with?