I haven't read that book about the Sven i Rosengård ballad either. And I'm not sure I know much about this ballad.

But anyway... Geijer and Afzelius in Svenska folkvisor från forntiden (Swedish folk songs from ancient times, 1814) give two versions of Sven i Rosengård, both are from oral tradition rather than from old manuscripts. They also include translations into Swedish of The Two Brothers (from Jamieson) and of Edward (from Percy). They also write that there is no song corresponding to Sven i Rosengård in Danish. And also that it is a "fragment of a genuine ancient Scandinavian song"....

Arwidsson in Svenska fornsånger (ancient Swedish songs, 1837) also includes two versions of Sven i Rosengård from oral tradition, nothing from older manuscripts. He also includes a translation of an "older" Finnish version of this ballad, called The Bloody Son (Den Blodiga Sonen in Swedish). He too is keen to describe the ballad as incomplete versions of a "genuine Scandinavian folk song".

The three versions of Sven i Rosengård in Grundtvig (in Danish) are all from oral tradition as well, the earliest collected in 1844. However, he also writes this: that (as well as 11 more recent Swedish versions from oral tradition) he knows of a manuscript in poor condition with a "half-comic" version of the text in Swedish, 33 verses, from the 1640s, and that this is in George Stephens's collection.