I won’t bother asking you what percentage of climate change is natural vs mankind induced.
By most of the definitions I've seen, 100%. Because it's defined as the change in climate caused by humans.
That said, rather than percentages, it's normally stated in degrees. 4-6F by 2050, for example. Do you actually NEED to run off the cliff and crash at the base in order to accept that there is a cliff ahead?
The problem with your demands is that to meet the falsification levels you demand we'd need to have duplicate earths in order to "test". If we had multiple earths, we wouldn't really need to worry about global warming...
As such, computer modeling is used(which has been refined tremendously since the '80s when we started modeling), continued observations, and falsifiable experiments conducted at smaller sizes.
Oh, and Hawkmoon, wood, what matches are made out of, is a carbon neutral fuel. As is most incense stuff. It's the coal, gasoline, and natural gas that is adding carbon to the atmosphere. Non-carbon energy sources includes nuclear, solar, wind, hydro, geothermal, and more. We don't even need to eliminate all CO2 production, just get it down to a level where we aren't threatening our ocean ecology(fish are good to have, right?), flooding coastal cities, losing much of Florida, etc...