i think the 2 turn doom is already too strong, especially on ferryman where he could hit the whole team. I agree with the way inspiration works, it should either continue as it currently is, or perhaps just not effect doom/bomb at all, but the problem isnt really inspiration, it is the doom not having enough turns to attempt a cleanse.
On a similar topic, doom states that it "deals a lethal amount of damage" so it should be prevented by invincibility or vanish, it should have a chance at prevention from Assassin Banshee, etc...