Thankyou, that was most refreshing to hear. Stay safe!
NGU doesn't cause "a split second of urethral discomfort or tingling", and I have no doubt your self-diagnosis (psychological) is correct. Australia's network of national sexual health centres is probably the most professional, effective, and all around best STD clinic systems in the world. (I'm sure they agreed that your previous doc was wrong about trauma!) If they didn't think you needed testing for M genitalium -- probably because your symptoms cleared up nicely with azithromycin -- you can take it to the bank.
And by the way, the 40% azithromycin failure rate is only for NGU caused by M gen, which in turn is the cause of only 10% of NGU. And your symptoms cleared nicely on azithro, which itself is strong evidence that you were cured.
I would not recommend further treatment with moxifloxacin or anything else.