Actually the dustup over heat transfer from the atmos came up in the context of "positive feedbacks" for water vapor -- not TSI..
I show you the preferred merged record of TSI.. Average increase from 1750 is OVER 1W/m2. From TrenBerth -- 1/2 of that HITS THE GROUND.. Where in the IPCC chart is THAT number? You mention TSI to a warmer and they show you a Sunspot cycle chart with the TSI removed. I believe that's what's actually in the IPCC dismissal..
Contrary to your assertion ABOVE ------
You would need that effect to have been taking place constantly since 1880 yet it seems to have not begun till well into the 21st century.
--- MOST of the TSI increase from 1700 occurred before 1900 or so.. It fits perfectly into the realization that Trenberth didn't produce an ENERGY diagram --- he produced a POWER diagram (units are W/M2).. ENERGY has a time element. Includes thermal time constants (assume them very long to equilibrium) and thermal storage (in the oceans, in the warming polar regions, in various configs of atmos composition of gases) which have largely been ignored. You "300 year LAW" of temp change invokes that reasoning.
And all these revelations about thermal inertia (heat storage, thermal time constants) and NOT expecting the temp to respond immediately are ABSOLUTELY applicable to solar insolation as well. The surface doesn't know nuttin about where that 1w/m2 came from..
MWP was NOT spotty over 500 yrs.. The proxy record isn't even good enough to discern "spotty".. Let's call it 300 years. I'll give you 100 yrs up, 100 down.. If the PEAK is comparable to the today's "anomaly" --- how is that NOT a comparable RATE over 150 years? BTW --- What caused it? Let's hear your short list of other significant forcings being ignored here..
The balance of CO2 cycling on the planet kinda echos your Stephan Crane quote.. There are 700Gtons/yr of CO2 cycling per year.. Man's bill comes to 30Gtons (also a bogus accounting that I highly dispute). We are still speculating on the limits of the sinks. Higher temps and CO2 probably is an enforcer for the land sinks. We are 4% of the total exchange. (I'd take out the cow farts in exchange for the plains full of buffalo that they displaced and not charge man for every forest fire and make that a MUCH lesser number)
Positive feedbacks are speculation.. Termites emit more methane than the current Arctic calthrate leaks. Climate science has no humility.. Believing that our 4% of the cycle is the deadly part of the 700Gtons/yr. Give me an example in the historical record of Catastrophic runaway warming fueled by positive feedbacks. ESPECIALLY one based on a 1.0degC trigger...