I am not almost completely convinced that the temps médiane is not to be found in Braudel's work because he actually does not care about the temporal duration at all.
What he cares about is the predictive value of the temporal categories; that is why the other category is the business cycles, where each iteration is short in temporal extension, but their re-occurrence makes them akin to la longue durée in that way.
Thus, there is maybe then not much point in being able to sort them in their duration, especially tracing them backward. It is at any rate not a lesson that Braudel wished to teach (whether it be interesting or not is a separate question).
This explains why the tracing felt like such a big waste of time emotionally, because it was unclear what it would contribute. Rather there is the general task of establishing the temporal bounds with respect to a specific degree of conceptual abstraction (to generate the identity that permits the comparison).
If we have a temporal problem that exhibits the pattern that we have [start,end] constraining the years of interest, it is hardly helpful to know that start-t or end+t still exhibited the phenomenon—without some analogizing or justificatory explanation, that is.
Rather the question is, does the problem exhibit stability during the time period. If we presume that this is an issue that has stable duration for the bounds in question, then there should be no variability; if we presume that it belongs to the cyclical patterns, then we should assume that we may have variance, but the plotting the "rise and fall" of the value in question will reveal additional useful information.
Whether the problem has stability or not allows us to settle the foreground -- background issue, and gives contour to the explanations or reconstructions in that fashion. The stability of course need not have been obvious to the participants, and the cyclical natures may not have been either.