While I am not a priest of the UGCC, I am a deacon. I admit I am also having a bit of difficulty in following the general trend of discussion.
What's the situation nowadays? Do they follow the proper Byzantine rite or they still have Roman rite influentions? Are these influences aproved by any local Synod and introduced in the Ieratikon/Slujebnik ?
The UGCC Synod has decreed the Ordo Celebrationis
obligatory; in addition the more recent Instruction
from Rome is also included in this category. This is echoed in the more particular law; for example the particular law for the UGCC in the USA specifically exhorts the parochial restoration of the Divine Praises, especially Vespers and Matins.
Actually a number of parishes are in the process of restoring more of the traditional liturgical cycle. An excellent example can be found at http://www.saintelias.com/ca/index.php
While there is still much to be done, the UGCC has come a long way since Zamosc, and much of that improvement happening in the last 40 years.