Contrary to popular belief names were NOT changed "when entering the US" Ship manifests were created at the Port of Departure, with info taken from immigrants passports which were obtained in their home country.
This is not to say that errors were not made, as they were. Also modern day transcribers mis-read info on ship manifests and other old documents.
If you notice the 1930 census states they came from Italy, as post WW I some of the western part of Slovenia was under the rule of Italyhttp://en.wikipedia.org/wiki/History_of_Slovenia
The 1930 census lists his immigration year as 1913 and hers as 1920
Name: Rosalio Bevcic
Arrival Date: 26 Jul 1920
Birth Date: abt 1900
Birth Location: Slovakia
Birth Location Other: senumo
Ethnicity/ Nationality: Slovakian
Port of Departure: Le Havre
Port of Arrival: New York, New York
Ship Name: Lafayette
The above is an example of errors, first the person who created the manifest at the port of departure mistakenly typed "M" in the Gender column and then corrected it by handwriting "F" over it. Then the modern day transcriber did not see the correction and listed her as a male.
Also the person at the port listed her as Slovak, which was a common error. Even today Slovak and Slovene are mistaken on some records.
She lists her next of kin at Semano Istria as her father Johann
Her destination is Thomas, WVA to her brother Jose BEVCIC
Also WVA records show her name as BEVCIC not BEVIC
The Slovenian spelling is BEVČIČ which sounds like bevchich.
And this would appear to be you GGrandfather
n Name: Johann
Last Place of Residence: Lpod Zemen, Austria
Event Date: 07 Oct 1913
Nationality: Austria, Slovenian
Departure Port: Antwerp
Arrival Port: New York
Marital Status: S
Ship Name: Vaderland
Lj has a sound like the ll in the word million.
Perhaps the Slovenian phone book online would be of help to you where there are 22 BEVČIČ listed, but none in Dolnji (which means lower) Zemon but some are nearbyhttp://www.itis.si/iskanje
The phone book is in Slovenian but if you have the Google page translator you can translate to English, otherwise in the box under kdo-kaj type in the surname the click on Nadji, this will take you to another page where you will select Osebe, this will give you a list of names and contact info.
There are 89 listings for GRILJ in the phone book Take a look in Ilirska Bistrica which is a place near Dolnji Zemon
Ilirska Bistrica is the administrative center for several villages inc. Dolnji Zemonhttp://en.wikipedia.org/wiki/Ilirska_Bistricahttp://www.ilirska-bistrica.si/turizem/http://en.wikipedia.org/wiki/Dolnji_Zemon
Hopefully this will help you in your search. In any case Slovenia is a beautiful country and I hope you enjoy visiting there as much as we have when we included Slovenia in some of our Croatian Heritage tours
Just an aside many Croatians, especially from the Zumberak area which borders Slovenian went to Thomas WVA in the early 1900s, some of those eventually came to Cleveland.
Croatian Heritage Museum