The incoming ice age could be averted by simultaneously adding carbon-free greenhouse gases like nitrous oxide to the atmosphere, but I suppose that kills the "solving global warming" part of the pitch.

Not all life is connected to earths atmosphere. That doomsday weapon is missing caves which contain multicellular life across geologic timescales. The ecosystems dependent on chemical synthesis at deep ocean vents would similarly be unaffected.

That's a good point and I don't see a way around it.