Then the part where I'm not at all certain about which direction the effect should be, is because while CO2 decreases thermal conductivity by radiation, it increases thermal conductivity by convection because the heat capacity is higher for CO2. Which is actually a much better intuition if you want to understand how does water vapor seems to have such negligible effect despite the fact it is a "greenhouse gas" and "absorbs much more heat".
You want me to point out bugs? There are like 20 different climate models. I've seen heat capacity being constant independent of pressure, temperature, CO2, density, etc. Not just heat capacity, but also other "constants". Not in a single place because the code is a mess, they actually have several different modules with different constants, so say the radiation simulation is extremely detailed mess that's completely unreadable, and the cloud simulation just starts all over with their own different constants.
Writing such code is somewhat human task, but reasoning about the magnitude of the mess that is going on there and which directions the errors will go is beyond the capabilities of anyone. It could be possible but not with the way it's currently written.
I'm sorry, but it is your thermodynamic intuition that's completely wrong. Equilibrium to you means "things stop moving". That... not how thermodynamics works at all. The reason that ordinary things look like they are "not moving" in equilibrium in your everyday life is because they do move, but at scales much smaller than you. Do the Brownian motion experiment.
And meta-stable states have everything to do with this, again this is your lack of understanding of physics, not mine. Given a thermodynamic system, there's expansion around the meta stable state or the unstable state over time, where you get the duration to reach equilibrium from the size of the fluctuations. The gist of the expansion is that what delays reaching equilibrium is that the fluctuations are too small.
There's infinite reasons why warming might be happening. Just the direction itself is a single bit of information with no significance whatsoever. It isn't worth my time arguing against a theory whose statistical strength is one bit.
The models don't have any significance beyond this bit or maybe two bits if you try to be generous about their abysmal performance regarding temperatures. They had some success at very high attitudes, but that's not surprising as these high attitudes are just so much simpler to predict and have no bearing on the rest of the model and the actual climate as observed on the ground. They excuse their shortcoming as the "weather", but if your models don't have any feedback from reality and testing around the parts that matter, why should I trust them ?