It's not that odes 1-8 of the orthros kanons are moved, I would prefer to say that the heothinon gospel is held back until the end of the 8th ode of the orthros kanon. That said, let's remember where the St Sabas Typikon places the heothinon gospel when it's called for in *any* orthros: after the anabathmoi and prokeimenon, which are *always* before the 50th Ps and the kanons. Right? Well, this is still the case in any church that follows the St Saba typikon (i.e. Mount Athos, I use them only because they're (mostly) Greek).
A short historical note. The place of the gospel reading in the orthros is not so standard down through history; bring to mind Gr Saturday Orthros. In the cathedral or asmatic rite of the Great Church it's place was at the end of the orthros, as well as it was in the early monastic daily offices. There are also a number of Byzantine mss with kanons that find the morning gospel placed after the 3rd, 6th and 8th odes. In fact, I just described a 15th c mss menaion that has the gospel for the feast of the Annunciation (25 March)check this outafter the 6th ode. The oder is as follows: the kanon of the annunciation, the same one we use today with the alphabetic acrostic, the kontakion and *all 24 oikoi of the Akathist*, after which the synaxarion is recited, the 50th psalm, gospel and then odes 7-9 of the kanon! It seems that this is the second placing of the Akathist, the first being on 26 Decemberthis explains why the acathist does not progress beyond the veneration of the magi.
Back to the subject. Second, how is it that the Biolakes Typikon places *only* Sunday heothina gospels after the 8th ode? The answer is that it's not really Biolakes. This seems to have become the practice in the patriarchal church of Constantinople by the end of the 18th century and, by extension, in all the parish churches that were under its spiritual care at that time. This we know because the first edition of Konstantinos Byzantios the Protopsaltes' Typikon (Constantinople 1838) places it in this very position. If you read the title page of the so-called Biolakes Typikon you'll see that it is actually the Typikon of Konstantinos that has been 'corrected' and embellished, filled out by a Patriarchal committee headed by Biolakes. In essence, it is a reworked, though not 'reformed', Konstantinos typikon. The point is, in the patriarchal church, even though the patriarch himself did not serve each Sunday, some patriarchal metropolitan did. The educated guess (there's really no bibliography here) is that since the metropolitan was not in attendance until a later time in the service, the order of the heothinon gospel was held back to its later position.
Conclusion. 'On what basis do the Antiochians fail to observe this separation?' The practical answer is that even if they are following a translation of the Biolakes edition of the Konstantinos typikon (I don't know this to be the fact, other than the earlier post by Stephan), it is quite possible the editors have (a) opted to move the heothinon gospel to its normal position in the Sunday orthros (as has the Church of Cyprus: cf. their Hemerologion) or (b) either at the time of translation or some subsequent edition the editorial committee for some reason felt it should retain the older practice. I can think of two reasons for the latter, (i) that was what they were doing anyway, or (ii) they're actually not following the Konstantinos-Biolakes typika, but the St Saba.
In any event, there is an historical precedence that is not in any way, shape or form arbitrary, but an authentic element of the same monastic, St Saba/Studite Typikon used by all Orthrodox Christians throughout the world.
Postscript. By the way, the reading of the heothinon gospel is done immediately after the anabathmoi and prokeimenon in all male and female monasteries throughout Greece, as the Konstantinos/Biolakes typikon was never meant to affect monastic practice. This can also be extended to monastery Metochia in large cities, like Athens and Thessalonike.