The main difference is in how one uses one's "other" judging function. E.g., does an ENFP use Ne with Te? Does an INTJ use Ni with Fi? And how does that look?
So it seems to me like you're more interested in how the functions interact with each other to result in functional categories that are separate and distinct from the original broader function terms. You seem to think that Ne and Ni alone are no different but rather are just made different by their complementary judging functions, right?
I believe socionics is more geared at examining functional interplay and gives more definitive merit to how the functions interact when making its categories, but that's just what I've heard through the grapevine. I don't really know much about socionics (it seems rather messy and convoluted to me), truth be told, but you might find that it's worth looking into.
Personally, I believe that I use Ni with Te, and that I use Ne with both Ti and Fi. This makes me believe that it is the "same N", but that the judging functions direct how things are perceived by their e/i attitude.
I think I'm understanding you, but correct me if I'm wrong. The premise behind your pet theory is that there are no discernible differences between Ne/Ni and Se/Si, but rather, the differences we see in cognition among SJ/SP and NJ/NP types come from the judging functions that affect the perceiving function in question. You believe this because 1) you think you personally use both N functions, and 2) the characteristics of the ENxP/INxJ dynamic point to shared cognitive values. According to your pet theory, 1 and 2 imply that Ne = Ni (and your theory says the same about Se = Si).
According to this categorization, that would mean that Pi paired with x judging function would cause the same cognitive values and attitudes that Pe paired with x judging function does (ie, PeTi = PiTi because Pi = Pe), right? If that's the case, then I'm going to have to disagree with your pet theory for now, lest you provide further support to back up your claim (though the part about implying that the examination of Ne, Se, Si, and Ni necessitates a complementary judging function for thorough understanding is interesting, and I'm inclined to agree). But in regards to Ni = Ne and Si = Se, I don't think that's the case (but I'm open to new ideas

).
INJs and ENPs have completely different cognitive attitudes, even when they share judging functions, so this implies that there's something else going on that distinguishes these two types cognitively. The only reasons this could be the case, categorically speaking, would be function order and different perceiving functions (Ne vs Ni and/or Se vs. Si) that the two types possess.
Since your theory completely undermines the Pe/Pi dichotomies, this would mean that your theory has to support that the difference between INJs and their ENP complements is due solely to a discrepancy in Je/Ji order. How can your theory use this discrepancy, without also incorporating opposing N functions, to justify the cognitive differences between INJs and ENPs?
Personally, I believe that I use Ni with Te, and that I use Ne with both Ti and Fi. This makes me believe that it is the "same N", but that the judging functions direct how things are perceived by their e/i attitude.
There are a lot of people on this forum, myself included, that do not believe Ne/Ni can be healthily juxtaposed, as the two are definitively in opposition with each other. Why exactly do you think you "use" both?
Other evidence is that for "compatible types", one switches the E/I, T/F, and J/P, but not the N/S. Thus INTJs and ENFPs find each other fascinating, but are not so attracted by ESFPs or ISTJs, respectively. In theory, ESFP should be a better match for INTJ, since they share all functions, not just two. It matters much more that one shares Te/Fi or Fe/Ti, and not at all that one shares Ne/Si or Ni/Se.
I agree with you that sharing judging functions is more important for compatibility purposes than is sharing perceiving functions. I get along with TPs and FJs better than TJs and FPs for exactly this reason.
However, I wouldn't go so far as to use this dynamic as "evidence" for your theory. It simply means that the judging functions may be more important than the perceiving functions in predicting the potential for effective communication and mutual compatibility.
ENFPs and INTJs may be fascinated by each other, but that doesn't have to be because they possess the same functions in a different order. We can justify this dynamic by saying that the ENFP's Ne instills a wanderlust for novel concepts and ideas and is thus intrigued by the new perspectives that Ni has to offer while the INTJ's Ni allows for constant shifts in perspective and thus is fueled by the creative connections that Ne offers. This Ne/Ni fascination, complemented by shared judging functions that allow for mutual understanding of each others' moral values, results in a fruitful relationship.
We can justify this dynamic by the function categories already in place, so this relationship is not necessarily evidence for there being no discernible difference between Ne and Ni. So, again, why do you view this as evidence in support of your pet theory (rather than as evidence in support of Ne/Ni being different)?