OK. You are an _NFP. I suspect INFP. For further reference, there's the site
INFJ or INFP? a closer look.
I say INFP because your Ne givaway has a certian "teach-ness" about it that sounds like a good parent (second function).
I know you say (and even emphasize) that you can logically construct/deconstruct things. By the way, deconstruct sounds more like Te. In fact, I'm not suprised anymore that you got a score for introverted thinking. This test is getting to be well known to give you the result of the process most different from what you do (except that they're both introverted judgement) (Linda Berens wrote an article about differentiating between extraverted sensing and extraverted intuition, I know that MANY improvisers mis-type as extraverted intuition types with that test. With that in mind, the test making this type of mistake again wouldn't suprise me at all)