Dear Harmonica,
Sadly, when the RC Church "shortened" its liturgy, UGCC bishops felt they had to "keep up with the Jonuses"

and do something similar.
So they introduced the POSSIBILITY of omitting the Second Antiphon and the Ektenia for the Catechumens and one more later on.
When that happened EVERY UGCC parish, save for a few more traditional ones, brought in the shortened forms.
My parish does not and if Andrew were in it, I think he truly WOULD feel he is in an Orthodox Church (in fact, the Greek Orthodox advisers to the film production "My Big Fat Greek Wedding" personally recommended my parish of St Nicholas as the BEST example of an Orthodox Church they ever saw - so THERE, Andrew!

).
There is not one tradition for each parish, but all the parishes I know up here in Canada have the antidoron and more (especially the parish of St Elias).
To be fair, one would find liturgical differences in the usage of the Antiochian and Greek Orthodox Churches and those of the Russian tradition.
The Latinization in the Ukrainian Catholic Church is not ONLY because of Latin influence - it was historically a deliberate acceptance on the part of the Ukrainian Catholics in an attempt to fight off the "Russification" movement emanating from the Orthodox Russian imperial empire - and later from that of the Soviet Union.
In addition, during the Kyivan Orthodox Baroque era, Latinizations were quite commonplace in the Orthodox Church (perhaps even moreso than in the EC churches). St Nicodemus of the Holy Mountain thought nothing of translating into Greek numerous Western spiritual works and he even refers to a practice of "Orthodox indulgences . . ."
Alex