Hmm. I'm not sure if you can change the key config if you put a controller in. I think it just goes to the default of... you know, P as the square button, K as X, S as triangle, HS as circle, and Dust as R1. Though, if you had a stick with a PS2 hookup, and plugged that into the controller port... would that also make it default to the same way you two play already? No idea! But it would be a fun experiment.
But yeah, I remember when I first learned GG at an arcade too. I mean, Kick on the top? What's up with that! Axl does not like mixing up Punch and Kick. And it made his counters weird too. The bottom button is for the high counter, and the top button is for the low counter. But oh well, I'm used to it now.
Also, I'd just like to emphasize again, tonight would be an awesome time for coming down. Why, it's a beautiful day here. The birds are singing, and the streets are filled with laughter. I even heard they were giving away free ice cream and puppies. It's totally the best time to come.