The point of this analysis is to illustrate the fact that there is nothing absolute or required about the relationship among ajnas, but on the contrary those relationships are culturally and historically determined, hence arbitrary (in the technical sense intended by Saussure in his Linguistics). Within Bayati Shuri one path was used, but disappeared and was replaced with another pathway, the one currently understood by most musicians. In both cases, Hijaz is the predominant secondary jins, occurring on the 4th scale degree above the Bayati root jins. However, the contrast between the two pathways occurs at the top of the scale.
First, it is necessary to understand the typical behavior of Hijaz: when it occurs as a root jins its primary modulations - to Nahawand and to Rast - occur on its fourth scale degree, so it behaves very similar to Bayati itself. Below is an example within Maqam Hijaz, where Nahawand 4 alternates with Hijaz 1, from the Warda song "Harramt Ahibbak":
(See more examples of Nahawand as a secondary jins; and compare the usage here with the similar use of Nahawand within Maqam Bayati)
The question becomes then: if the melody within Bayati Shuri is to go above the Hijaz Jins, where will it go? Should it rise up to Bayati on the octave, thus maintaining octave equivalence? - this is the modern solution. From the Muwashshah "Hibbi Da3ani lil-Wisaal":
But if we follow the expected Hijaz pathway (shown in the example above from Maqam Hijaz), instead of Bayati on the octave, we should find a jins Nahawand on the fourth scale degree above the Hijaz tonic, which would be the 7th scale degree above the root Bayati tonic - disregarding octave equivalence entirely. This is precisely what we find in the 1931 Umm Kulthum song "Mihtaar Ya Naas":
It is worth observing that octave equivalence seems to have been much less of a priority in the early 20th century, than it became later--because a number of maqamat from early recording history display a complete lack of octave equivalence. Only a few examples are shown on this site, the Maqam Dalansheen of "Ijma3 Shufna" and the Maqam Hijazkar-Kurd of Tif ya Durri, but there are numerous instances of this among early 20th century maqamat, and a gradual disappearance of most of those pathways by mid-20th century.