I vote Kf1
Martin vs the world analysis thread #4

9. Qd2 Bb4 Bc1 Nxe4 Qxh6 and he now has to check our King immediately or play Bh7. (or we play Bh7+ for the win)
11. … Bd2+ 12. Bxd2 Bd7 13. Nxe4 and Martin is lost.
So, it appears Martin cannot take our e4 pawn. All of this is to spark interest on Qd2.

That's good work, I definitely like the tactical play there, but there might be problems. He doesn't have to play 10... Nxe4, he can wait to pull that trigger. If instead 10... g5, he shuts out our queen and now really is threatening Nxe4. He also has Bh7 himself to block our bishop from teleporting there, and add an attacker to e4. So I still think Qd2 is bad.

The problem with Kf1 and h3 combined is that our rook is very sad on h1. I prefer Kf1 if we're playing h4 in the future, giving the rook a way into the game. But can we play h4? Or is control of the g4 square too important for us?

I think e5 is our best move. It's not really opening up the e-file, if he captures he doubles pawns on the e-file which is a hinderance for him, not an asset. After e5 dxe5 Bxc5, it gives us superior pawn structure and at first glance I can't see how it benefits him other than to develop a piece with tempo, ie Qa5, but after Bd2 our position is solid, our weak e4 pawn traded off.
If he chooses not to capture the pawn, then he has to move his knight, which takes away both Ng4 and Ne4. This gives us time to castle.

Tug, I'm not hooked on Qd2, but it does bring out the tactics of this extremely sharp variant game. The 5 checks and teleporting Bishops make the Bishops like Queens. I'll give e5 a look… the more we play with the pieces/events, the better we'll understand the extreme difficulties of getting a solid advantage. This game is near impossible to calculate, btw.

Yeah the bishops are very powerful here, I definitely think they're better than rooks.
The problem with Qd2 is it puts our king and queen on the same diagonal, which he can load up on with Bb4 and Qa5. e4 is an ongoing weakness for us. That position above is horrible for us, g5 sucked the life out of our plan. If you can find a play from here, that's great. I'm definitely happy to be proven wrong. I hope between us we can find the optimal move. But if we find a problem with a move, we should assume Martin will also find the problem and exploit it. We can't bank on him missing something we didn't miss. He'll find g5, no problem.

Bb4 looks better than Ng4 to me. I don't see what Ng4 is doing, other than attacking the bishop. So we move it to g3, then play h3, and he made no progress.
Bb4 puts his bishop on the same diagonal as our king and queen. It should be obvious why that's good for him and bad for us.

If we play Qd2, he might play g5 before playing Bb4, as it also prepares Bh7 or Bg6 to pile up on e4. I think both g5 and Bb4 are fine for him in response to Qd2, he likely plays one then the other.

Kf1 does deal with the problems we face, but it causes us development problems and it's unappealing.
e5 is my preferred move at this moment.

Starting to like e5.
9. e5 dxe5 10. Bxc5 Qa5 11. b4 Qa3 12. Nb1 Bc3+ 13. Nxc3 Qxc3+ 14. Bd2 Qa3 15. Qb3 Qxb3 16. axb3
or 14. … Qd4 15. Nf3 (attacking Black's Queen)
15. … Qb2 16. 0-0 Bc2 17. Qc1 Qxc1 18. Raxc1
Black's Bishop needs to flee, Queens are off the board, our King is safe, we are about to go up a pawn, both our Bishops remain, but we have two checks on our King.
So, it seems that 10. … Qa5 (trying to infiltrate) will go nowhere for Martin.
What else can Martin try for 10. … ? as a result of our 9. e5 pawn push.

More on e5...
9. e5 Nd7 10. e6 fxe 11. dxe Nf6 12. Bf7+ (1) Rxf7 13. exf7+ (2) Kxf7 14. Nf3
It is a safe bet that Martin must capture e5 with 9. … dxe5.
9. e5 dxe5 10. Bxc5 Nbd7 11. Be3
I've moved the pieces around, more than my notation shows, and in every instance I find nothing wrong with 9. e5. Generally, when I try (and try, and try) to find something wrong with a potential move, and nothing comes up, then it is a good move. 9. e5 carries a threat and improves our position by getting rid of weakness in pawn structure. It buys us time, allowing us to hope that Martin will "blunder" or make an "inaccuracy."
Conclusion: 9. e5 is a candidate move.
Now on to Kf1… … investigate it.

I've looked at Kf1, not too deeply but while it does solve problems, it creates more problems in the process. We lose castling rights, and our rook on h1 struggles to find a way into the game, especially if we play h3 instead of h4. I'm not a fan of Kf1 unless there's no better alternative, and it looks like we have that alternative in e5.
sorry I haven't been calculating i've been too busy calculating martin vs tug