I've listened to the following octave displacements ("8D") that both professors intended to be easily identified, at least 20 times. But I still can't. How can I correct this hearing flaw?
I don't think it's a hearing flaw that you can't recognise these versions as easily as the originals. After all, the original intervals are gone, and the original rhythms are gone. The only thing that remains intact is the scale degrees. So one suggestion would be to learn scale-degree functions, as suggested in this answer.
If you think you might have the aptitude, developing a sense of perfect pitch might also help, though I'm not sure how easy that is (there are plenty of other questions about perfect pitch on the site).
If it's genuinely your aim to recognise octave-displaced tunes, you might consider just playing a few simple tunes yourself, firstly with more mild octave displacements, gradually becoming more extreme. As well as attuning your ear to octave displacements, it could be a good exercise in navigating your instrument!