Thanks for showing this with a whiteboard and diagrams. My professor did nothing but scribble a few sentences on the board and talk for an hour. You're a prime example of youtube being a better source for education than my actual university.
I believe your construction is probably good supporting material for why the undecidable/looping bit appears for the constructed machine, but your argument for that isn't clear to me. You also haven't clearly described why the constructed machine and the blank tape machine have output/decidability equivalence.