I'm so sorry you were hospitalized and hope you are feeling back to your normal self soon.
I'm far from an expert on PSLF, but I have former students and friends who are on it and they have definitely changed jobs. My understanding is that you need 10 years of payments while working full-time for any qualifying employer, not the same employer for the entire 10 years. The denial rate is high but I heard it's because they're so quick to reject people for paperwork errors. So you have to be really careful but you can also appeal your denial!
Anyhow, your main point still applies--PSLF is way too complex for what should be a simple straightforward way to help the many people working in public service with overwhelming student loan debt!