And (2) we need to execute that method under controlled and verifiable conditions and yield a significant score of prediction.
To show that TA works I don't think "controlled and verified" conditions would be a feasible experiment. You'd have to round up every Bitcoin trader in the world and somehow control them, because they are the "conditions".
You have a point here, and this brings up the question if this is a matter of science and specifically of exact mathematical science. But there isn't just math and physics, there are also the moral sciences and there is technology and engineering. Each of those has a way of precision.
Indeed, personally I rather see TA as an proposed / alleged method of technology or engineering. And it is quite common to run field tests of various kinds to verify methods and procedures in technology. In this context I had in mind, "controlled and verified" means that the conditions are controlled to an extent so that the experiment could be repeated, which of course includes some management regarding the knowledge of the subjects involved into the test.
In situations where self-suggestion of the test subject is important, often some kind of blind test or even double blind test is applied. Transferred to our situation, this would mean to conjure up some trading strategies, which look superficially correct, but are wrong or ineffective, based on the methodology of TA. And then, in the practical test, the traders executing these placebo strategies need to do significantly worse than those employing the real TA based strategies. And, as a point of reference, some strategies based on random choices need to be included as well.