For any query, I'd like to get results in e.g. JSON that contain 'abc:XYZ' rather than 'http://my.domain.com/data/XYZ'. Is that somehow possible without own post-processing?
Not really, the server returns full IRIs. However you can use some standard utilities, e.g. RDF4J’s JSONLDWriter, to print RDF in JSON in a compact form. Stardog 6 won’t use (and ship with) RDF4J but it will provide its own RDF writers for the same sort of purpose.