I currently work for three local governments. One clearly employs me but the other two I’m self-employed. Is there any way to count self-employed work that is otherwise eligible toward PSLF?

I don’t think so, if by “self-employed” you mean you are contracted by the government. However, if you’ve classified your self-employed business as a qualifying business (non-profit, etc) you may be able to get your own business to count, but they would require supporting documentation.