Sorry Dr. Super Evil....
I have tried what you suggested and instead of placing the timed life behavior that has the damage response on the Spawn Effect field, I put it in the SET effect of the Ability and it still does not work. Caster still gets credit. I have gone over what you have said and I'm 90% sure I have done exactly as you described and it still gives the kill credit to the caster and not the target.
If you review the test map it is clear the target is also getting the kill credit buff applied to himself VIA the damage response and the caster gets the buff first before the target buffs initial effect kills him. It should work in theory according to what Kill Credit is supposed to do but it doesn't.
If anyone reviewing this has an idea of why or can prevent a solution I'm all ears. Until then I'm going to have to give up on the solution as unsolvable at this point.