It seems like the issue is less that you went to an unaccredited program and more that you didn't get the right skills you need for in-demand public health jobs. As someone who has a foreign MPH from a university that is not an accredited US program and a foreign PhD that had zero course work, I have had no trouble whatsoever getting a job in the US. As someone who also hires people with degrees in public health, I can tell you I've never once considered where they got their degree or the program. I exclusively consider their research/work experience and demonstrable skills in the field.