Does your grandmother have any Vitali brother's still living... or any of her brother's sons? If one of them would take the Y-DNA test, then you could compare their haplotype with the broader Jewish population who have been tested and possibly the Vitali Jews that Braverman mentioned to you. There may be other more efficient methods which I'm not aware of yet, but that is my best suggestion.
You could also start a FamilyTree DNA "Vitali" Y-DNA Project which would encourage Vitalis to test and join, maybe even reluctant Vitali male relatives (if you have any still known to you). Click on the FamilyTreeDNA link and then go to the Projects link and you'll see better what I'm suggesting. I didn't see a Vitali Y-DNA Project started yet when I checked.
Hope that helps!
Regards,
Hanok
