You've probably figured this out by now, but if it isn't clear to others, I've been arguing that I agree with you even if I disagree with Han's character.
If you choose to view Han as a rip roaring badass, Greedo shooting first doesn't make him less of a badass. If you choose to view Han as a softie in denial, Han shooting first doesn't make him any more cold-hearted.
I view him as a bad ***, but I think people invest far too much in one single scene. It's not like he engages in a drawfest EVER again, so the Greedo incident is not part of a larger pattern which defines his character.
It's an isolated scenario that means little more than "Guys like to shoot me cause I owe money and I'm just lucky. Or bad ***. It doesn't matter what it is, so long as I'm alive."