I do not think you have any grasp of "proof" based on what you write over and over. If you do, you hide it very well. You're repeatedly saying false things and expecting them to be taken as fact. Scientific illiteracy, repeated endlessly, does not become fact. If you find that abrasive, maybe you need to be .. abraded .. a bit.
How is it done? "Giant ballroom" .. is actually closer than you imagine. A virtual giant ballroom anyway. It is done the same way real science is always done. Gather evidence, analyze, write it up, and publish in an established journal. The journal is, in virtual terms, that ballroom. If your evidence is solid, if it is repeatable by other scientists, and if your analysis is correct, your claim will be substantiated. It will be scrutinized, probably painfully, in detail, questions will be asked probably via responses in other papers / journals, and you'll have to be able to address them. This is not for intellectual babies with easily hurt feelings, the processes are brutal .. ask Ketchum, ask J. Harlan Bretz, etc. Ketchum was refuted and ridiculed because her science was garbage. Bretz' work was rejected for decades but finally accepted and now is the mainstream understanding. If your work is good, it stands, if it is crap, it falls, and that is how it should be.
There is no shortcut. If you're not going through the established processes you're not going to be accepted by the establishment. Until that happens, you do not have proof regardless of what you wish to believe.