Thank you.
Gary, just in case you are not aware, because Michelle, your fellow Serb-US citizen, was not, if you can read Cyrillic, you can check all people who were either permanent or temporary residents in Belgrade roughly 1919-1952 and there are quite a few Baraćs there, I believe close to 150. Perhaps one or more of them are distantly related to you.
Check
https://www.digitalni.arhiv-beograda.org/ and then in the drop down menu choose "Register of Inhabitants...". You will need to register but is is fairly straightforward. I discovered data about a relative I was looking for there and bumped into one I had only vaguely heard about previously.