Crucial point 2: Sparda reborn; common theme of eastern mythology is a hero returning to be ready when he's needed most, reincarnation is a common belief of eastern religions and faiths, especially in Japan. You have no idea how this became a misconception in the Zelda fandom that the various heroes are just the same person reborn over and over instead of a common trait being referrence by "Spirit of the hero" being a figuritive phrase as a result of knowing this aspect of eastern faiths. Also...why would a quarter breed be possibly more powerful than a HALF breed, or be transforming physically into a demon? Even Bingo's novel kept flipfloping on what was actually going on, to where Nero figured that his real form IS demonic, and his human form is just some kind of chryaslis form like a caterpiller transforming to a butterfly(and that was the NOVEL'S wording), and Dante even said "I don't care who your parents are, I just care about who you will be." The novel contridicted itself repeatedly, so, yeah, Deadly Fortune contridicts game and it's own narrative.
Crucial point 1; There was no indication in DMC4's story outside of of Bingo's FANFICTION novel that Vergil ever visited Fortuna; LADY was the one who told Dante about the city, and made him interested because they worshipped his father. In fact, we have no indication that it was actually Dante who was in the library, that was Nero's assumption. The only reference to Vergil from Dante is just that Yamato had belonged to "my brother", but remember that it is above all else a sword of Sparda, same with Rebellion. Vergil is never even referred to by name.