You might find that Scythians are actually a stronger presence than you might think; there's evidence that Sogdiana had a relatively large population of 'settled' Scythians or Scythians tied by alliegance as far back as the Achaemenid period. Bactria and Sogdiana have always had a somewhat complicated relationship with the steppe nomads.
Now, the problem with the gymnasions is this; when the Scythians and their amigos invaded Bactria, they pretty much destroyed all of that. Ai Khanoum, Alexandria Oxiana, was pretty much razed to the ground and this was a monumental city that may even have functioned as a capital. Their treatment of the other major Hellenistic centres of the kingdom does not seem to have been any kinder. So the question is; where do these gymnasiums come from? By this point, the 'elite' identity in the kingdom is no longer Greek, so why would he be interested in propogating an identity that is not associated with the ruling class?
In this period in actual history, the Kushans are only just getting going as a real state and the Greek identity in the area was still relatively strong (if no longer an elite identity). We still get coinage issued in Greek style, though there is a steady growth in Bactrian inscriptions that use a modified Greek script for an Iranian language. So I think you can probably assume that little enough time has passed that there are relatively numerous descendants of the various military settlers of Graeco-Bactria and probably that Greece continued to be a living language (although not for much longer). It seems the prevailing theory is that the Hellenic elements of society continued to be used by the Kushan state afterwards, but I haven't seen any paper or book that properly discusses what this might have entailed or that provided evidence for it. My point is that it's possible that Hellenistic-style warfare continued to be practised by militia forces, levies, and perhaps some professional elements.
They probably missed out on some of the later Seleucid reforms of infantry, so if they want to remain relevant Hellenistic infantry of this state will definitely need to modernise. I would have thought that some of the older hoplite/phalanx modes would survive in elite units like Agema if they're being revived, but that you'd see a shift towards the 'imitation legion' style (which actually weren't imitating the Romans but that's a different matter). What Bactria lacks, so far as I know, is the technology to produce steel. Iron is certainly found nearby, in the Bamayan province of modern Afghanistan. But I'm fairly certain the Graeco-Bactrians didn't have steel, and I think that might prove a problem given time. The first evidence of crucible steel in Central Asia isn't until the 8th Century AD OTL, as far as I know.
I think that placing the state as the middle-man of the China-Europe trade might be work as a way of spreading culture both ways. I do think that a Hellenistic state existing in a living form in Central Asia again would probably have a lasting impact; even the OTL Hellenistic presence there had consequences for the development of India and Central Asia.
One thing I would say is that demographically, it would still seem that Bactrian will eventually eventually triumph in some fashion as a written language. It's spoken by the largest group in the core region of Bactria, and I don't really see the other Indo-Iranian languages making significant inroads here. I think it's definitely going to become a vernacular language, but I think you can justify Greek remaining administratively and as a prestige language.
I think you definitely need to establish how Greeks transition into becoming an elite group again, from what amounts to a standing start.
Interesting interesting, great stuff. To respond:
- In this timeline, I'm assuming/imaging the Scythian penetration into Bactria as slightly more pacific than OTL. The major push that resulted in the Kushan Empire hasn't happened at the start - the Indo-Greek kings are still there with their tiny principalities, Indo-Parthian realm of Suren is there at the start, etc.
I've worked in marriages between a conquering Yuezhi chief with a Greco-Bactrian princess, to account for OTL appearance of Greek elements (perhaps indicating Kushan descent from the Eucratids or Euthymids) on Kushan coins. So we have a prince, Sapadbizes, who has some "Greek" blood and is perhaps literate in Greek, who is competing for ascendancy in the region against a rival chief, a half-brother called Pseigacharis. The Parthians briefly take back the Bactra oasis, placing Cleopatra there; the abandoned Cleopatra eventually invites Sapadbizes and his men to come forth and join her. The marriage provides Cleopatra with much needed protection from her enemies and provides Sapadbizes with a dynastic/imperial legitimacy before the remaining Greek élite. He thus styles himself King of Kings and sees himself as a viable successor to the crumbling Arsacid, Seleucid and Achaeminid lineage, in no small part thanks to his partially-Seleucid queen. I'd like to think that such a sequence of events, and particularly Cleopatra's charismatic presence, would strengthen Greek identity, both in the reborn/newfound state and its young king. As Sapadbizes unites the Indo-Greek kingdoms, the Saka and the Yuezhi, settling more of his Yuezhi bethren further south in Bactria and beyond, there is less destruction (or none) than OTL. Beyond that, Sapadbizes actively patronizes and builds gymnasiums, where the local ephebes are educated and subsequently drafted into city militias (perhaps providing him with those 'Greek' infantry units we talked about?) and civic administration. Whether Bactrian, Indian, Scythian, Iranian, these young men get educated in both martial arts and a smattering of Hellenistic knowledge, enough to advance them according to Sapadbizes' desires.
I should also mention Sapadbizes not only marries Cleopatra in this TL, but also visits Rome, Mediolanum, Greece and the Roman East, perhaps influencing greatly his conception of empire and Imperial displays of power, military organization, etc.
My thought is that Sapadbizes will therefore draw more heavily on Greek/Hellenistic tradition than his own paternal culture, encouraging the rest of the Yuezhi/Saka elite to intermarry yet further with the Greco-Bactrians and Hellenize just as much or more so than OTL.
As for steel, I think there might also be iron to be found in India. Contact with Rome and Arabia perhaps facilitates the spread of the necessary technology?
Beyond this I'm imagining Cleopatra, even after her departure, acting as a sort of Bactrian Arsinoe II, establishing the prototype of both queenship and monarchy overall. Drawing also from Argead, Seleucid and Arsacid traditions, where marriage to women of the royal family gave men a share of royal power, resulting in frequent incestous marriages (half-sisters and step-mothers are attested as far back as the Argeads) by new monarchs seeking to stabilize their throne. Here, the legitimacy of Sapadbizes' claims to kingly status and Seleucid succession derived primarily from his marriage to Cleopatra - creating a mold for his successors to follow, in marrying the "rightful heiress" as a means of securing the throne and establishing their own superioty over the client Indo-Greek kings and lesser chieftains of the Saka and Yuezhi.
I could go on and on


but that's the rough outline so far. Alas, no Tocharian or Manichaeism...right now I'm think Greco-Bactrian and Greco-Buddhist revival
