Yes, it seems correct.
Traxler QE7 Lines virtually ALWAYS WIN in KF1 Variations
But how about 9. d6 instead of 9. c3?
Pawn just takes, and the threat of bg4 and qf6 is still inevitable and black king can escape checks by the bishop
9. d6 cxd6?? 10. Kxf2! and now black has no threats.
If Kxf2 Ne4+, King simply goes to g1. If Qh4 threatening mate on f2, Qf1, both defending and threatening Qf7+ with support from the bishop on c4 and knight on h8, so black is forced to play something like Ng5 to defend, then white can offer a queen trade with Qf2, and even if black tries Ndf3+, followed by Kf1 (NOT gxf3 because of Nh3+ winning the queen) Qxc4+ d3, white is up a full rook and doing just fine, while black has run out of steam.
Correction, after Ndf3+, gxf3?? Nh3+ simply mates. But of course, that's why white plays Kf1 instead of gxf3.

And at 11...kg1, black could also play D5, preparing Qc5 threatening double checks and mating nets. That's the one I was forgetting. But thx for bringing up d6. That one is interesting!
11. Kg1 11...d5 12.Bxd5 12...Qc5 13. Bxe4!
Surprisingly, there are no good discovered checks!
Exactly. Black runs out of steam quick, so long as white doesn't screw up.
Actually I feel nearly compulsive about playing the traxler counter-attack after I discovered. I actually have the worst results in the Kf1 variation. I crush the Kxf7 line, but Kf1 I lose most of the games. I will study this thread, as it will hopefully help.

But how about 9. d6 instead of 9. c3?
Pawn just takes, and the threat of bg4 and qf6 is still inevitable and black king can escape checks by the bishop
Pawn just takes is just a mistake. Taking with the queen is correct, and Black is not worse if he knows his homework.
But who cares about the stupid 5.Nxf7?
Black can easily equalize and white is behind in development, AND black has potential tactics
White EASILY loses and is Forcably Mated most of the time