No, I said that the professor’s emphasis on the math and not on the conceptual aspects of his thought experiment is what led to his mistake about the A clock “ticking faster”. He neglected the Doppler effects of the light signal and he made some other conceptual mistakes. He relied on the math and the light signals, and that led him astray. If he had used the more direct method of the dropping marbles, he would have realized his error. I’ve always said that if the conceptual stuff is not correct and not understood, the math, perfect though it might be, is useless, such as in Section 4 of the SR theory.

Regarding the “closed curve”, you seem to think that Einstein was thinking that the clock slowed down during the closed curve. I’ve read in several books that acceleration does not affect balance clocks in that way, like it affects atomic clocks, and, anyway, Einstein wasn’t read yet for acceleration considerations in 1905.

“So far we have applied the principle of relativity, i.e., the assumption that the physical laws are independent of the state of motion of the reference system, only to nonaccelerated reference systems. Is it conceivable that the principle of relativity also applies to systems that are accelerated relative to each other?” A. Einstein, 1905 (“Collected Papers, Vol. 4, page 301)

I think it would help if your understanding of this difficult subject if you would buy a few more pertinent books.