Indi to me this argument looks like a good example of how a little knowledge can be dangerous.
I think it is great you are using maths and physics to try to make your point, but without putting them into the systems framework, connecting all causes and effects to the relevant inputs and outputs, it doesn't prove anything, though you can present it as if it does, really what you are doing is creating a sales pitch, comprising parts of the truth, but not the whole truth, which is a different story.
I think you are doing this with the best of heart, but you / we are all conditioned to do it by the old zero sum system, which always demanded losers cease to exist, if they could not contribute towards further enriching winners.
If Sri Lanka could not take loans to be paid back with interest to the IMF, or any other loaning body for example, it would be seen as not "Pulling it's weight", and the colonial powers in the West would just say something to the effect of "just f-off and die please". You know what I am saying here is true.
Dooming, without showing any way out, can only prepare folk to oblige those that wish them dead.
Losers, who can't or won't contribute to winners, for whatever reason are supposed to just disappear.
Can you see that this, systemically, is the thing mathematically unsustainable?
The old system does not require infinite growth to survive at all, as long as it survives, it only needs the losers who can't keep contributing, to keep disappearing, and you are unwittingly assisting it, by adding to the conditioning needed, for folk to just quietly lie down and die.
To me it is cool you seem driven to learn, but not so cool if you are only interested to learn what you might need to support the old system conditioning.
Learn more about the systems of nature and humanity, and you start to see how we are just being born as a species, from a system of limited energy, to a system of relatively unlimited energy, in the same way as anything born, a chicken from an egg, a mammal from its mother, or a plant, from the energy of Earth.
The plant is the one most resembling the transition we are making, from the energy of Earth, to the energy of the environment of Earth, the sun, so the plant is the one we can learn most from.
It is true folk don't need to have PhDs to understand this.
But we do need to understand the whole systems view, to be able to make fully reasoned arguments one way or the other.
That takes some time, in my own case more than 30 years learning and practicing Systems Engineering, and a lifetime of nearly 60 years just learning how to get busy living, rather than being busy dying to oblige the old system.
I hope you might make better progress than I did, actually I am sure you will, but the more you write about dooming, before learning how things actually work as a system, the more work you will have to do to undo the conditioning of the old system.
Conditoning, coupled with lack of systems knowledge, is what makes you argue that we can heat up the planet by putting more solar energy to our use than less, and it is easy for me to debunk that argument by reminding of say, Einstein E=MC squared rule, that says effectively energy which is not put to use as material, is what manifests as heat.
If we are creating materials and things from energy, then by definition we are converting that energy to things other than heat.
Creatiion, is the opposite of creating heat.
A planet which is busy creating next to a massive heat / energy source, stays cool in response to the heat energy landing on it, whereas a planet which is dead, in the same situation, simply heats up.
Our planet heating up, should indicate to you that it isn't that we have too much life on it, but actually the opposite, life is dying on Earth, we are killing it.
Too many humans is not the problem at all, actually it is our activity of destruction which is the problem, and the real thing mathematically and physically unsustainable.
To reverse it, we simply have to move from destruction, to creation.
I hope you won't see my comments on you personally as any kind of attempt to personally undermine you. To me it's just another part necessary of the systems analysis, the part we formally identify as the stakeholder analysis.
To know how to fix things, we need to understand incentives and motivations.
As long as we are motivated by the requirement to make profit, then we will tend to reinforce the old system of destruction.
Remove that, by issuing the free money required to monetise the economic product already created by the use of solar to date, and the incentive of all people has to change, from one of wishing to preserve the old destructive system powered from the limited energy of Earth, to one of getting busy creating in the new system.
After that our species in creative mode might grow to many times it's current size, but creating, cooling, instead of destructing, heating.
Why should we expect it not to grow to some kind of mature adulthood, naturally tailioring that to our new energy environment , like anything born?
BTW, on lithium mining, creating hydrogen fuel from solar removes pretty much all requirements for batteries therefore removes the need for bulk lithium mining that some argue will be needed for the future.
Further, conversion of that hydrogen to "Solein", removes enough human demand for food from the conventional food chain, by providing an alternative for humans, for the food chain of nature to recover.
Technology isn't the problem dude, the problem is having to do it for profit, just like you maybe need to write for profit.
Get rid of that, and we get rid of all the problems.