TDHXIII:
I think you will not be shocked to hear me say that what I think you are supposed to learn from this is this:
If you pay as little attention as possible to all that
noise, you might find yourself in a dream without
ever needing to remember to roll over into it. This goes for RA as well; come to think of it, it goes
especially for RA, because if REM Atonia has truly set in, then you are
already in REM, asleep, and ready to dream. Also, if you take the noise a bit less seriously, that distracting "cringy feeling" you experience will be less likely to happen.
So I think what you should do next, particularly if you feel like RA has ensued, is try to remember that the reason you are doing a WILD is to lucid dream, and not to experience all the noise. Try to keep your thoughts and attention focused on the dream, and not the stuff going on around you. If you can do that, and manage to stay calm, patient, and open to your coming dream, you might discover that you were never actually stuck on a last part of a technique, but were already hovering at the threshold to your dream only to deny yourself entry thanks to all those interesting distractions.
And yes, your hearing tends to work just find during sleep, so external sounds can be audible during dreaming.