Just play:
6.Kf1 Qe7
7. Nxh8 Bc5 (If Nxe4, then 8. Qh5+, g6 9. Nxg6, hxg6 10. Qxg6+ Qf7 11. Qxe4)(If 7...Qc5, Then 8. Bf7+ Kf8 9. d3 Bh4 10. g3!)
1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 Bc5 5.Nxf7 Bxf2+ 6.Kf1 Qe7 7.Nxh8 d5 (only move according to theory and played at GM level) 8.exd5 Nd4 reaches the main tabiya of the Traxler 5.Nxf7 variation.
Also according to theory in OP's line, his opponent played suboptimally and could have won immediately with:
5.Nxf7 Bxf2+ 6.Kxf2 Nxe4+ 7.Kg1 Qh4 8.g3 Nxg3 9.hxg3 Qxg3+ 10.Kf1 Rf8 intending 11.Qh5 d5 with an overwhelming attack.
How do I win against this opening?
I lost one today