For greater clarity on this issue, here's a very different way of looking it:

Let's suspend, or forget, for a moment, the differences between how MBTT and Socionics see the various building blocks ("functions" in Jung/MBTT, "IM elements" in Socinoics), and look at this purely from a Socionics point of view.

Seen that way, MBTT reflects simply a hypothesis that an emphasis on static IM elements would tend to cause one to be less inclined towards schedules and externally-directed order, whereas dynamic rational IM elements would cause one to be more inclined towards schedules and externally-directed order.

Why would this be the case? It's fairly obvious: dynamic elements are all about sequence, things moving through time. Dynamic rationality (Te, Fe) is all about externally-directed order. This is why Ej types tend to be what some people might described as J-like. That doesn't mean that they're organized (organization of things would be a static quality), or even that they're on time....but they would be oriented towards sequence and externally-directed order. For example, I would expect Ej types to be most comfortable with stopping an activity because of some other planned event that comes afterwards.

Similarly, Ij types may be inclined to "weight" static order over externally-directed dynamic order. For example an LII might spend time learning the more of the system involved in doing a task than is actually required....or might decide not to go to some scheduled activity because he/she is in the middle of organizing something (preferring to focus on static order rather than dynamic order).

Where the problem is, however, is that this MBTT-derived theory tends to ignore the fact that strong emphasis introverted dynamic functions (Si and Ni) may also lead one to be less inclined towards externall-directed order (Ej).

If a person has given less weight to externally-directed schedules, the question needs to be "why": Is it because one was learning or working out a system or categorization, and this was more important than the external event (a Ti-reason)? Or is it because one was just daydreaming or enjoying the moment (answers that may be more typical of IEI or SEI, for example)?

Similarly, Ij types may, in some cases, be so organized that externally-directed schedules aren't a problem (think of the often punctual LSI type).

This explains both a) why MBTT's analysis of J/P isn't crazy, and b) why classical Socionics goes in a different direction...that is, why the J/P switch isn't necessarily valid regarding types.