Kyp's personality was formed through the infinite sadness

"What good is being a Jedi if we don't act?"
He wouldn't have been who he was in the Old Order. there he would have been taken as an infant and trained away from his parents. He would have become an ordinary Jedi. This would have been a NR time and thus his parents wouldn't have be dissidents and wouldn't have been mprisoin ed or killed. So thus Kyp would not have known Kessel, imprisonment, and the sheer hopelessness of an uncertain fate and indefinate slavery. With none of these things to build on and no mistraining by Luke he would have been a very differenent person. He most certainly would have lacked the anger and thus even the level of passion of Mace Windu.

Think about what shaped him:

1. Being raised by dissidents during an oppressive empire
2. Arrest and immprisonment at age 8
3. Working in a spice mine with your parents who can't protect you
4. Losing your parents at age 9, opossibly seeing their murders
5. Spending 7 mnore hopless years imprisoned, starved, beaten, mentally abused and uncertain if you would live or die
6. Escaping to only find that you are interrogated and sentenced to death by Imperialists

All these things would lead you to feel helpless and one way to combat the helplessness is to find empowerment. How?

As a Jedi Kyp could help the enslaved, the oppressed, the exploited and the helpless. So he might be zealous about it, but he feels it is his obligation. It is likely he would be behaving this way even if he had never turned dark. Kyp acts out of a need to protect the galaxy, not to neccessarily atone for his crimes. Having once been so limited with little hope , it is understanding that Kyp would develop the mindset:

"What good is being a Jedi if we don't act?"

He'll carry this ideal throughout his life and choices.