The Romanian Maramaros district archives holds a lot of parish records from the Zakarpattia district.
Open the link below and scroll down til you get to 'inventare on-line', then open links containing the word 'matricole'. If you go to the end of each pdf document there is an alphabetic listing of the towns for which they hold parish records http://www.arhivelenationale.ro/index.php?lan=0&jud=102
Unfortunately to my knowedge FHL has not yet filmed any of these records. You would need to hire a Romanian researcher to gain access to these archives.