Not sure why you specify 7 life when any amount above 1 would accomplish the combo. It's possible that on its release, we will get a ruling for this card that choosing the same previously chosen card won't reset activate only once per turn abilities. But it should work as you hope.
Edit: The Rules Manager talking on social media has proclaimed that Koh does not work like this. Whether this is part of a rule change or rule clarification is yet to be seen. 11/11/2025
I control Koh, the face stealer which has exiled a kami of jealous thirst and an eager cadet. I have 7 life points and have drawn 3 cards this turn. Is my opponent dead?
Edit: The Rules Manager talking on social media has proclaimed that Koh does not work like this. Whether this is part of a rule change or rule clarification is yet to be seen. 11/11/2025