There were plenty of very convincing criticisms of the old Levi work
Was there? Where was it published?
My answer is that the original work is just as fraudent as the later work. Why? Because it stands to reason.
This is experimental science. Nothing "stands to reason." Any claim stands or falls by experiment only. There are no other standards. You have to have technical reasons to justify your assertion or you have nothing.
The Levi experiment was not replicated so we have no way of knowing if it was real or not, but just saying "it stands to reason" without listing technical reasons is not science. It is your unsupported opinion. It is also not debatable or falsifiable. How would anyone show you are wrong? If it cannot be falsified, it isn't science. The same goes for THH's claim that there might be an as-yet undiscovered error in Fleischmann's experiment. That's true, and it applies equally well to every experiment in history. There might be undetected errors in experiments done by Galileo or Newton, but it is exceedingly unlikely. While it is true there might be an undetected error in Fleischmann's work, you cannot make that claim in a scientific discussion because it cannot be either proved true or false. THH has to point a specific error and show evidence for it. A negative view does not get a free pass. He, and you, have to support your assertions with as much rigor and as many facts as anyone making a positive assertion does.