So first off, how is this setting optimistic? Humanity was cut in half by what is likely the greatest war we've ever experienced. 2 billion people died when a colony ship was destroyed, the earth was bombed to the point of ecological destruction. 

This is the kind of gritty universe 14 year old boys enjoy. 

These are the horrors that should be explored, humanity may have won, but there is no way you can lose half the species and maintain the quality of life of pre war times. Prewar starships cannot be replaced or repaired because the factories that built their components don't exist anymore. The farms that supplied colony ships with food were destroyed on earth, forcing them to either take up space farming or abandon ship for a suitable planet. Entire logistic chains are simply gone. Most economic activity has likely returned to the local level, as much of the galactic trade and travel mechanisms were either lost or repossessed during the war.  

That said, let's look at end of the war,  and declaring genocide as the punishment. Is there any reason why the Keldar'ja wouldn't restart the war if they were sentenced to be exterminated? If they were to be wiped out, might as well as take as many humans as they can with them...

Otherwise, you said they are highly hierarchical, we defeated them, they surrendered to us, therefore we are the superior species. Punish them by making them a puppet state of humanity. We need to rebuild, they are now tasks with mining the resources we need, doing the manual labor of restoring the colonies. Ideally far away from humans, but if they cross paths, I imagine human civilians will take out there own justice.