Other than quitting your current position, calling in sick and/or using vacation or personal days to job hunt/interview, what are some ethical and doable ways to look for a new job or career?
I’ve found a number of positions for which I am qualified. I have my bachelor’s degree from a top-tier school, so finding the job isn’t really the issue. It’s finding the company that will interview or consider me with the crazy schedule I have currently.

I have had good luck just telling prospective employers about my situation. If they are interested, they will often have a first i-view via phone, let you come in on your lunch, or after work.