The fact that cultural diffusion goes in both directions at the margins does not disprove the existence of cultural diffusion, or that the culture with the greater scale and advantages generally ends up as the dominant influence. They still stayed mostly Ymaryn, and retained the bulk of those core values despite their lifestyle significantly changing. The Stallion tribes are also deep, deep in the past, when the Ymaryn core was vastly smaller and less influential.
The cultural superiority of the Ymaryn manifests in different ways to the Greco-Roman one. We have organised religion in a way that they didn't, and we have much more sophisticated technology, which, given it will be like/is magic to outsiders will have the same kind of impact.
Marrying into and getting our hooks into the Storm Ymaryn nobility will also give us routes of influence that the Romans were very unwilling to use, as the children of barbarians weren't considered Roman, and it was unusual for them to try things like inviting foreign princes for a Roman education. The Ymaryn education system would be the envy of the world, and our patricians could invite their Storm Ymaryn nephews to attend.
Uh, nooooo.
ERE had very,
very powerful monotheist Orthodox religion. In fact, its strength is one of big factors which made them so influental on Rus - it gave legitimacy to Rus rulers and basically is, likely, the biggest factor behind such influence.
Ymaryn religion is too syncretic (as opposed to Orthodox, well, orthodoxy and strict interpretations and traditionalism) to be nearly as powerful a cultural influencer as Orthodox christianity was. In return we gain faster spread and flexibility which allows it to evolve with times and bend instead of breaking as times go by. But still, we are never ever going to impose our views on other people via Mythaladism as well as Orthodox church could because of how flexible and open-minded it is.
And another aspect which makes our religion worse as a medium for cultural pressure than Byzantine orthodox church: it is, well, comparatively weak. We do not have a lot of temples, and they are not all that big. When we have several dozens big temples, or
at the very least a big temple in every single big city we can talk about using it as a vector for cultural influence.
Before that...well, look at Highlanders. They took our religion's theological skills and instruments
and none of our values and teachings. That's how "open-minded syncretic organized religion without a shitton of temples to back up one particular version of it" is going to go: inject its skills and a bit of values into the next generation, and that's about it.
Again, you are just not willing to invest for the sake of achieving goals. Yes, it is possible to go full Byzantium and culturally influence everyone into imitating us purely via passive cultural pressure - but you need to correspondingly invest into culture (Theaters, Libraries), religion (Temples, Libraries), advanced knowledge to impress people with (Libraries, Academies, Temples, Observatories) and so on. Plus, well, establishing relationships (Diplomatic Missions or at lest Diplomatic passives).
It is certainly possible, but again, it requires investment. No free lunch here.
