I know you've seen the following two video links before. When you make engines as capable as these, or better, using your theories, people will be more willing to listen. Until then you will get a lot of opposition. Be very kind to those that stop to listen, and even kinder to those that enter into discussions. You have nothing to lose by doing so.
In the videos it is very important to notice the correlation of heat flow direction, absorption, rejection, and to the rotational direction. It is important to notice the description of the head difference between engine and refrigerator. And this was all done in the 1940's and 50's. This is the closest I have found to your requested information. Temperatures blatantly obvious and at large differentials.
https://m.youtube.com/watch?v=GqIapDKtvzc
https://m.youtube.com/watch?v=GFfMruoRMGo
Reading the comments helps too.
They were successful using the Carnot theory and Kinetic theory. Kinda puts an acceptance on those theories.
You keep claiming that lots of heat is being dumped to the cold plate, in Carnot theory, but the theory doesn't speak of 'amount' of heat. It speaks of proportions of heat, energy, temperature, Work, COP, and Efficiency. It could be only one percent efficient and pump only 1/10 Watt to the cold plate. Producing 0.001 W of output power. That is very close to what LTD engines do produce, when under load. Less when run free.
The Carnot theory is based on W=Qh-Qc. You have only measured temperature. Your Qh value isn't Qh, it is total energy to the heat source. No measurement as to where it actually goes. Assuming it goes into the engine is a bad assumption. You have no value for Work, or Qc. No way of determining efficiency. A.K.A., Inconclusive.
If the theory is useable, it is not bogus or ludicrous. At least until a better, more useful, and accurate, reliable theory comes along to replace it. And then the old theory may still be used where appropriate. Flat Earth theory is still used to build houses, buildings, bridges and dams. Round Earth Theory is needed for building long roads, ship and aircraft navigation, space missions, etc.
Me being skeptical, of the premature conclusions you put fourth from poorly done home garage kitchen experiments, and instead, using 200 year old consistent, useful, and productive, standard thermodynamics, is hardly being in denial of science or hypocritical. Please...
I have a lot more than a "double standard", when questioning science, and even more for other things. Scientific papers, people, and practices are not all created equal. LOL. In fact some writings are intentionally fraudulent. Some are called novels. Fun to read but my scientific standard is very low for them. Furthermore, the papers that have obvious contradictions and logical errors, get pushed low on the score list too. However, I do weigh them from other viewpoints as to if there is anything of merit despite the errors. Call it the Feynman effect. Find the errors and learn more
Your twisting of evidence, inconsistent logic, slippery slope and other logical fallacies are very plain to see.
If the Carnot limit is 20%, the reversed Carnot will have a COP of 5, ideally. The two hooked together will return 100% of the heat back to the hot source, removing all heat rejected to the cold sink. That is acceptable constant theory.
If you hook a new engine to that reversed Carnot that is 21% efficient and of the same size and other constraints, it will return 101% of the heat back to the hot source. This is called, "Over Unity". Over unity from an engine with only 21% efficiency. Ideally. In reality all three real machines will have half of those values, 10%, 2.5, and 10.5%. They are in no danger of going over unity.
The worst part is I hope someone does build an over unity machine. It just doesn't seem likely. But I don't want to discourage anyone. We, humans Earth, need it Trying to do so will be a great learning experience. It was for me in highschool with capillary tube investigation. Please build, keep building, and above all be rigorous, and comprehensive.