With a surname like Zupancic, you will need to narrow down the area of search, as this surname is very common throughout many parts of Slovenia. With a name like Anton, and especially John or Joseph, you may end up following the wrong family entirely. Were John and Mary married before they left Slovenia?
The surnames Oberstar and Tomsic can be found around the area of Ribnica and Dolenja Vas p. Ribnici. While there are a number of Oberstar in the capital of Ljubljana, the surname is more or less indigenous to the Ribnica area. There are 15+ Oberstar in Ribnica, and some in Dolenja Vas. Similarly there are 15+ Tomsic in the Ribnica area. While there is only one Zupancic in Ribnica, the surname is more common in Videm, which is only a few miles to the east.
However, I would try to exhaust all the records available in the US before starting back in Slovenia. Have you checked the intent to naturalize, or similar records such as death certificates. There may be a place of origin noted there.
Hope this helps.