kork and workin-on-muh-stach, I really empathize with your sensitivity to repetitive noises, feeling trapped (and thus anxious), and desperately needing to have a tranquil, predictable living space. For me, it's rooted in a history of domestic violence; my dad would beat the living sh!t out of my mom late at night, and as a child I was frequently awaken by screaming, sobbing, and police cars and ambulances. My brain is wired to be on constant alert and no amount of good therapy will rewire it (for me, antidepressants help). Bessel van de Kolk's book, The Body Keeps the Score: Brain, Mind, and Body in the Healing of Trauma, has been extremely affirming of my experience and profound need for tranquility in my home.
As for noise-canceling headphones, I've found Bose wireless noise-masking sleepbuds to be the best I've found, both as regards comfort and noise cancelation. I bring them whenever I spend the night anywhere away from home. They've been a life-saver... worth every non-mustachian penny.
Good luck and take care.