"Doing the liturgy differently" is something of a misnomer. Certainly there are superficial differences in the rubrics which developed in different national churches over the passage of many centuries. Likewise, the modality of rubrics are different within the national churches today from various points in history. What you saw in Hagia Sophia in the 11th century might not be completely familiar to a modern eye or ear, but it would likely resonate with some sense of 'sameness.' The same can be said if you attended liturgy at a Serbian or Antiochian or any other American jurisdiction. The differences from the olden days would be far greater than the external differences among our jurisdictions.
What you will not find within Orthodoxy is the range of differentiation in the liturgy which you may find within the Roman Church - ranging from a rapidly recited 'low mass' to a guitar mass 'novus ordus' to a Tridentine High Mass and any and all variations in between them.
As WRO struggles to establish its rubrics, I suspect that some form of uniformity will come out of these efforts as well. Perhaps the concept of a 'reverse uniatism' might be not serve as a direct analogy, but there are some Orthodox who might seek to impose Eastern liturgical norms that were not 'regular' in the west prior to the schism in an effort to make the WRO appear 'more Orthodox' to our eyes and ears. That would be the reverse of 'latinizing' however....
I think I pretty much understand, and am in agreement with, what you are saying except for your use of the word "reverse". Even if WRO were "uniatism" (and I believe I share your skepticism about the possibility that it is
) I don't understand why anyone would call it "reverse
uniatism". That's like saying that if I punch you it's "reverse punch" because a "punch" would be if you punch me.