You're a numbers guy and I'm a concept guy. I am not going to make excuses for the shoddy university work.
The basic concept is right. Input from the Sun must match the output from the Earth, whether it is directly from the surface, or a step further from an atmosphere.
The atmosphere will have an insulating effect with or without GHGs. That means the surface must be warmer.
The numbers they produced are obviously flawed, and to claim all atmospheric warming is due to GHGs is atrocious. But the basic mechanism is there. I should read the text that goes along with the graph but I couldn't be bothered.
I know that you are focusing on the concept, but I also know from what you posted in the past that you disagree with the numbers the IPCC cranked out so far.
For example the serious discrepancies in the proxy series you exposed a couple of years ago.
It turned out that the concept using tree ring proxies is not any better than using what the groundhog did on groundhog day as a climate proxy.
Overall I do not disagree with the concept as you lay it out, but somewhere along the line that has to be expressed in numbers.
If we use empirical data then we have to rely on the tree ring proxy and M.Mann speaking as the master of ceremony for the Yamal tree instead of the groundhog.
So the best way would be as you suggested as a step#1 to start out with a sphere that has no atmosphere and hash it out what kind of numbers we get with the numbers we picked for the factors that determine the outcome for step #1.
There is no way to avoid picking some numbers like for example the albedo.
There is also no way to short circuit the thermal property and the mass that has to be warmed during a 12/24 hour exposure cycle using the StB equation....and proceed by using an average value between the maximum and the minimum for that cycle.
I`m looking forward to see what you and others who wish to discuss the step by step concept you suggested have to say regarding step#1.
One thing is for sure the way the U of Washington "solved" step #1 is ridiculous.