In my head, I picture Alex sitting on the stool with the hat on his head and his BIG FANART EYES and before the hat can say anything Hammy's all "THERE'S A THOUSAND THINGS I HAVEN'T DONE JUST YOU WAAAIIIIIT!" and the hat goes "Ayup, this one's for Godric."

There are Slytherin traits in him! I just picture the line between them that Slytherin's think honor is mostly an artificial construct that is largely malleable depending on the circumstances and Gryffindor's would NEVER SACRIFICE HONOR JUST TO WIN HOW DARE YOU.

But, you know, fandom. Variable. :D