I had a bit of an unfortunate experience with an academic institution where I completed the coursework for a theology Ph.D. without high enough grades to continue. There were other things that were unfortunate about that experience, but the best advice I have been given is that if I try to return to studies, I need to explain why I don't have a reference from my previous Ph.D. programs, and if I document things that were wrong, that comes across as "I am a negative person who will publicly backstab a university by criticizing it after exhausting his appeal options" rather than "XYZ happened and if you can document it, we will make accommodations." (Additionally, I've tried to document the talent I have, but documenting that I am talented, no matter what talent I document, doesn't seem to trip any light bulbs of recognizing I may be a promising student.)
In graduate school admissions, what is a convincing non-negative way of explaining "I don't have references from my prior program?" And is there any way to get connections made between "gifted" and "promising student"?