otello has played this endgame remarkably well. If that was all instinct, we have a Capablanca on our hands.
To be honest, I use the analyze game feature to play out every possible permutation I can think of (my skill level limits me in this regard, obviously). I measured this set of moves several times to queen my pawn before starting the process. OTB, it would be very difficult for me to process that many variables.
This would explain why we've had a game going for a month now and we've only finished like 10 moves. I tend to take awhile analyzing moves too.
My problem with the analyze game feature though is that it doesn't limit you to legal moves. I've done some analyses where I've totally missed that someone was in check for like 3 moves

. I have another site that I use on my laptop to play around with rather than using the analyze game feature, when possible.