Using Jung's original definitions makes my type all the more obvious. My comfort zone has always been in the
inner world. Regardless of how enthuiastic I may get, or how long my posts, how much I post, etc (all of which taken as "external focus" by some). And my focus is obviously
logic. Even if it appears to be used in an "extraverted" manner at times, by definition, putting these two factors together, it still matches Jung's "thinking introvert".
The other method acknowledges that a lot of logic is being used, but declares it "extraverted" because of the working with existing concepts and the extensive rationale used to prove it all to people (where Ti analysis is presumed to always be kept internal, to be concise, and come up with new concepts), and "childish" because of the enthusiasm. So then, you have to prove a less apparent Fi is really the preferred judging function, in the "parent" position. This is done by searching for any form of emotion or valuing, including even expressing likes or dislikes. This seems to lend itself to a notion of INTP's as "Spocks", who apparently do not have many likes and dislikes, or do not "know what they want".
Even valuing of and enthusiasm over logical things and theories is said to be Fi, even though it is traditionally characteristic of NTP's! 
(Ironically,
Beebe himself said in his "An Archetype Model of the Self in Dialogue" (which I finally purchased), that all functions make valuation, and that F is simply the one that places the highest premium on assigning value!)
Continuing; Fe is forced into the Critical Parent, with any negative use of it as proof. But then, inferior can also be negative; the Anima archetype even described by Jung in a similar fashion as the witch/senex:
Jung's Archetypes
The Anima may appear as an exotic dancing girl or a weathered old hag--the form generally reflects either the condition or the needs of our soul presently. Remember the wicked witch encountered by Hanzel and Gretel. The Animus may appear as an exotic, sensual, young man or as an old grouch.)
So all of this creates
ambiguity. Then, the struggle to figure all this out is used as proof Ti is "trickster".

Also, the perception functions must be forced into the spines (as opposed to the arms), which involves the difference between Ne as hero or parent, Si as puer or anima, Ni as opposing or critical, and Se as trickster or demon. These also are very ambiguous, as those pairs of roles are very similar.
So this is what I had been sorting through since I've been here. There seemed to be great evidence for either side. Except that the type this latter method suggested simply did not fit! And the other type ended up seeming questionable, because of its characterization as unemotional! So I was really in a squeeze! And no further information or details from Beebe explaining how these things are resolved could be found.
This influential system was also the main method used here, earlier on in the Mistyped TYPOc Members thread, with Solitary Walker and Edahn the biggest targets. (SW because of his long posts interpreted as Te/Ni).
Others commenting on T/F questions would always affirm "T's can be emotional, everyone values things...", etc. and that seemed to be the general consensus based on experience or common sense.
The problem for me was that I had seen an intricate, systematic model proving the "hyper" view, and did not see any solid theoretical proof of what these others were saying. So it often sounded like a cop-out, borne of admitted ignorance as to how these "exceptions" all fit. The most you would get would be INTP's attributing their emotion to "inferior Fe". But much of what we mean by "emotion", and especially liking things, involves
personal values, which is defined as
Fi. So how do we explain this with the theories? Is the INTP going into demon/transformative mode everytime he enjoys something or gets angry or sad? It just did not seem right. Or maybe we just go back to the old view, that nothing is certain beyond the first two or four functions.
But to undertand the eight archetypes as
complexes removes all of this and makes it all simple. According to Lenore,
a T does not have to "use" F when having emotions. It's
just apart of being human. She says that our dominant function (whichever it may be, and I think in another place she says, any differentiated function) gives us emotional investment in what we're doing. I do not hold her view that the complexes only come out under such severe cases as ego-disintegration. I believe milder forms of the complexes do come out in lesser forms of stress. Which is basically what the standard Beebe view says. So I so still indentify with the Puer Si, Opposing Te, Critical Ni, Trickster Se, and potentially destructive Fi.
The difference is that they
are "complexes", and that not every use of the functions has to fit the archetypes, and also, not every apparent instance of the archetype role ("critical", "double-binding", etc) indicates the function playing that role.
I'm still not sure about the good uses of the shadows (backup, discovery, comedic, transformative). Berens briefly mentions them, and elfinchilde on the Spam Pudding mentions them when a shadow function comes up strong on the CP test. (The positive side of the shadows are said to manifest more when the processes are strong or "developed"). To Lenore (who sees "differentiation/individuation" differently than this), the Demon and Trickster manifest more constructive uses when the ego is ready to grow.
So for a couple of others here; Evan is also definitely a Thinking Introvert, with iNtuition. Just because he used Feeling a couple of times does not override the evident Thinking dominance. And since the "function attitudes" are more about the
person's orientation, than something attached to "the
functions", then with his obvious inner focus, and both Thinking and Intuition his preferred functions, it would be easy for him to appear to be introverting his intuition at times (especially if his genuine Ni is stronger. Mine is very weak, so I have no illusions of preferring it).
The same with SW--Thinking Introvert, who expresses his thinking in a way that seems extraverted at times, and his intuition seeming introverted because he's so focusing on his inner thoughts that he does not seem to be exploring external possibilities in his pronouncements.
Greed is an intuitive Extravert with Thinking (moreso than any Feeling). Little Linguist is an intuitive Extravert with Feeling.
So I'm not abandoning Beebe's model; just toning it down a bit. It cannot be used to describe our every perception and judgment.
Does anyone else find this method more helpful to them in finding a best fit type?