Hey Chester, you sort of answered your own question here, and it isn't a source of data, or scientific evidence you search for. There have been so many studies and research work, drilling ice cores in the arctic, accurately measuring sea temperatures, and on and on. In the third paragraph of your question you then state, "...explaining away the energy budget diagram and its trangressions seems more believable..."
Humans don't make decisions logically. If I asked you what 2 + 2 was, you would say 4. If I typed it into a calculator, it would give me the same answer in the same microsecond. If I asked the calculator what the square root of 174 is, it would also give me that answer in a micosecond, but it might take you 5 minutes to work out that answer with a pencil and paper. The human brain does not operate in a binary mode, it works to find patterns, and it frequently finds them where none actually exist, like dropping 100 pennies on the ground and seeing a cluster of them in one area that are all heads. You can give the answer to 2 + 2 so fast because in 1st grade you memorized your math tables, you don't have to picture 4 apples on the table for that one.
The "definitive" proof you look for is not something that should "seem" right or wrong, but all humans, including yourself, need to feel good about the proof, whether it's correct, or more accurately, correctly arrived at. Remember, it was just 1998 when a team of doctors and scientists stood on a stage on national TV and stated, "There is no proof that smoking cigarettes causes cancer." Did you believe that then? Do you now? Today the question is whether or not climate change is man made. Twenty years ago the question was, "Is there climate change?" Many people, most notably U.S. Republicans, were convinced there was not. Today even they believe there is, but we didn't cause it, and the natural conclusion is that there is no need to do anything about it since we aren't causing it. There are people in other countries that believe carbon emissions had nothing to do with climate change, but they do not belong to a particular religion, political party or sexual orientation, the division cuts across all classes pretty evenly. You are correct that the science is not settled, but what defines settled science? In our world, apparently, it's settled when most of us, "feel" the same about it. Personally I think we've already missed our opportunity to "do anything about it." We've been heavily carbonizing our environment since the late 1950's, only now is any measurable evidence becoming apparent to our patterned minds. My concerns are the same as they were in 1970, burning coal pollutes the air with particulates and chemicals, the water with mercury, and the ground water with arsenic, lead and selenium. These problems are enough to do something about it, why do we need other data? I applaud you for doing your research at NASA, NOAA and such. I suspect that as you continue to look into it, you will continue to find conflicting results, until one day you can decide that it looks like one result or another. Just remember that what appears to be definitive proof to you, won't to most other people. Most of us are too busy legalizing marijuana and outlawing vaping, for scientific reasons of course. Take care Chester, Rudydoo