Those holes may not be gaping ones.
The Family History Centre of the Church of Jesus Christ of Latter-Day Saints has microfilmed birth, marriage and death records from the Greek Catholic church in Velyka Plavucha. Unfortunately, they are only for the years from 1835 to 1865, but could prove to be a highly valuable resource for you. Let me know if you need further information or direction on this.
I can also refer you to a very reputable genealogist living in Ukraine who may be able to fill in the gaps for you. Although I have not used him for my research, I know others who have. He has a high degree of integrity, his rates are very reasonable, he delivers solid results, and he does not require full payment up front.
He is located in the Ternopil' oblast, the same as your ancestors. He is adept at navigating the Ukrainian archives bureaucracy, which can be cumbersome and frustrating to non-native Ukrainians.
Let me know if you're interested in pursuing that direction, and I'll provide you with his contact information.