OK, I listened to most of it, and he has re-iterated a couple things I have already said.
1. At around the 46:00 mark he clearly says that math is not physics, and physics is not mathematics, as I have maintained all along. He also says that math need have no "meaning" at all, but physics wants to give meaning (substance) to the math (form). And that's why I prefer LR to SR. There is no comprehensible consistent "meaning" to SR that does not violate other known laws. The math works, but the "meaning" is senseless. He says the "language" of math must be translated into words, and applied to the world, for purposes of physics (but not math). This is a point I have also made (and which you contested by claiming that it cannot be put in words, but only math).
2. He also says that there are many equivalent theories, and no one can be said to be "right" unless they make different predictions, as I have said. Therefore, in the context of SR vs LR, SR cannot be said to be "the correct theory."
3. He says, around the 49:00 mark, that the "rigor of mathematics" is not very useful in physics and that the physicist will be guided by "common sense." He goes so far as to speculate (and believe) that once more is known there will be no need for math in physics at all.
Most of Feynman's lecture on SR is expressed in words, not formulas. The concept that "the moving clock slows down" is NOT mathematical. The question of how much it slows down, at different relative speeds, IS mathematical. But again, the math is derived from the conceptual premises. The conceptual premises are NOT derived from the math.
Lorentz did not first discover the formula, and then deduce the "problem" it solved. He had a problem to solve, proposed a possible solution, and then quantified that solution with math. The (verbal) theory came first.
The problem: How is it that we can KNOW the earth is moving (by orbiting the sun, for instance) but not detect it?
A possible reason: because time and/or length changes with speed. OK, so how much would those things have to change to get this particular result? That's a SEPARATE question, which requires math to answer. But it isn't, and wasn't, the fundamental question. Math is simply a tool for physics. It is not physics.
PS: I have now listened to the whole thing.