Ok, there is quite a bit wrong here, and I think a big part of it is that you don't know much optical physics and things like black body radiation work. If you understood these things you'd realise how much you are saying is factually inaccurate and contradicting itself.
I guess that's inevitable if you try to skip to studying atmospheric physics without studying fundamental physics first.
Because of this, you don't really seem to understand what I wrote in my previous comment. In fact you are thinking of things only in terms of conduction and convection, and because of that coming to some very weird conclusions.
For example, if you understood some of this stuff, you would know that the blackbody radiation emission spectra is very broad. And so the amplitude at 15 um is only about 20% less than the max peak. So there is still heaps of energy there.
I'll try to explain in a different way.
When thermal radiation leaves the Earth, it leaves it at the speed of light. If we lived in a world with no greenhouse gases, then nothing would stop that energy leaving. How much energy is in the Earth's surface blackbody radiation? You can look it up or even calculate it if you know how, but it is somewhere between 20-30 Watts / square meter / steradian. Quite a lot.
This is the blackbody radiated energy only. Not the energy passed on by convection or conduction or the energy generated from anything else.
If there were no green house gases, this blackbody energy would leave the surface and get into space at the speed of light. It doesn't conduct itself through the atmosphere in the way you are thinking. It just goes. The speed of light is about 300,000 km per SECOND. So that energy would leave the planet in less than a millisecond.
This is why satellites can take instant photos of the surface, because the atmosphere is clear in the visible band. The light goes up instantly. It isn't slowed by conduction or convection. Thermal radiation is just photons exactly the same as visible light.
However, when there are green house gases, that blackbody energy gets absorbed by GHG molecules and passed on to heat the rest of the atmosphere. At that point, if the energy gets passed on by for example convection, that would be the speed of wind, which is in the range of tens of km per HOUR, and not even blowing directly upwards. So now the heat will leave at a rate of at least 40 million times slower.
Forty million times slower MINIMUM!
And that's just the thermal energy from black body radiation. We haven't even considered things like the reflection of the sun's infrared emissions.
You can't ignore radiation when developing a theory of atmospheric cooling.
I think you need to step back and read a book on optical physics before we can move on and talk about the atmospheric effects that rely on that physics.
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