A comprehensive post, but I disagree that the graph proves human activity will cause warming in the future. The general relationship that graph actually shows is that a warmer planet holds more co2. If co2 didn't cause any warming at all, that graph would still make sense.

The reason it is known that human activity will cause warming is because
a) we know the recent co2 spike is human caused beyond doubt,
and
b) the physics for why a co2 rise causes warming is also beyond doubt

Current evidence suggests that co2 and temperature are related in a positive feedback. A warmer world holds more co2, and more co2 causes a warmer world. The ice core record graph shows temperature rising about 10C from glacial to interglacial periods, while co2 only rises about 50% during the same period. The 4th IPCC report puts the warming effect from doubling (ie 100% increase) co2 as between 2C and 4.5C. Lower than can explain all the warming in the ice core record.

I think skeptics (or at least the reasonable ones) accept that co2 causes warming, but say it doesn't cause much warming. Problem is that the physics behind the 2C-4.5C per doubling range is complex and those ranges are the output of climate models. Obviously it's not possible to replicate a climate model in a discussion.