My guess, based on little other than a gut feel, is that while a lot of explosives were dropped on Tokyo, the energy was not concentrated enough to lift the soo

My guess, based on little other than a gut feel, is that while a lot of explosives were dropped on Tokyo, the energy was not concentrated enough to lift the soot high enough to be a global problem. But also, 1.6Mt just isn't that big a blast if you're talking nukes. Yes, it's bigger than current individual service warheads, but not by all that much. The B83 goes up to 1.2Mt. To put another bound on the question, Krakatoa was estimated at 200Mt in a single blast, and that definitely did affect the global climate. Again gut feel, but my suspicion would be that many distributed explosions around the globe totalling 200Mt would be worse in terms of direct effect just because there would be more physical mass available to be thrown into the air. Plus the soot would be radioactive.