I was recently forced out of a PhD program at XX early in the dissertation stage. Without going into details, XX acted in bad faith and also broke the law. So even though a good academic case can be made for re-admitting me, XX won't touch me.
The problem is that in order to avoid a lawsuit, XX manufactured a story about how I repeatedly failed to make progress despite their leniency. All additional information contradicting this story was deliberately omitted from my file and the people who know what really happened will not go on record about it.
So the only option is to enroll somewhere else. But it looks terrible to have been thrown out of a program after several years, with the official reason as failure to make progress on a dissertation. It probably also looks terrible say that XX lied about that, even though that's exactly what they did. I have good evidence, but an admissions committee is not a courtroom jury and will probably not want to hear that XX broke the law and lied to cover it up.
What can I do to address doubts about my ability to complete a PhD? Do I tell them what actually happened?