I think Nxe4 is actually a "line" that has been researched -- I think it's included in a footnote in my manuscript on the Traxler. I recall that it gave a couple of lines, one of which refutes it from the white side, so it's not good for black to play.

Poor play by white (no offense). Good analysis and depth of variations. This refutation removes your castling right (had white played correctly) with Bxf7+ but you have equal chances

6 ... Bc5?? is a MAJOR BLUNDER!!! ( but it's minor in this position)

6 ... Qxf2# was the correct move

Was this a blitz game?