We've discussed this countless times – phrases like "influenced" or "didn't influence" create a ton of borderline situations that lead to arguments.
Therefore, we should either use the phrase "not allowed, period" or allow rush strategies. As an alternative, we could allow them starting from turn 141 (at that point, it doesn't really matter anymore).
It's fun to read – two demons died or 1.5 times more (meaning as many as three demons were lost :))