I've pondered trying to "recreate" a hypothetical Jewish form. It just seemed pretty much impossible to divine what was Jewish from Jewish Christian. Like I said earlier, it strikes me as a series of verbal dioramas. They may not have even been drawn from a single original document. IOW the Christian author/redactor may have collected material from separate works and married these with his own. Without at least some guidance, it would be impossible convincingly separate sources.
You may have read that Cerinthus was one of the proposed authors. IOW, It was apparently at some point anonymous. The name 'John' is the single reason it was eventually included into the Canon of most churches. It seems reasonable to say that it was added to facilitate its inclusion into the Canon. Even then keen readers recognized the style differences from the Gospel and so assumed it referred to a different John. Eventually the Orthodoxy firmly established the tradition that the writer was the same man as the author of the 4th Gospel, the epistles and the John from the Gospel story.