Regarding the reasons why various parties killed for Genesis, my angle is simply that Saavik blames David for taking action (or perhaps inaction) that resulted in deaths, when this was never something David could control, and thus he cannot be argued to have killed anybody. Khan, Kirk and Kruge form a competing category in two ways: one, they all actually did
physically kill people, and two, they all had a choice of some
sort about the matter.
Khan chose to be an aggressor through and through, with no aims other than causing suffering (even his own crew critiqued him for that). Kruge's agenda was more complex, as you point out. Kirk had the choice between protecting the Federation from Genesis and Carol and her team from Khan and David and later Saavik and Spock from Klingons and generally doing good, and fleeing. I wouldn't expect Kirk to flee, and I don't find any fault in him killing the people he did kill. But while there are such nuances, he is still very much part of the category that Saavik could (and perhaps should) blame for the Genesis deaths, and thus the exact opposite of his own son.