Failed the preliminary PhD exam because the committee members rejected my already accepted publication
The advice to find a different university is probably the best you will get. The standards of the committee are apparently very high, as one would expect.
You could appeal to your advisor or to the committee, but it seems doubtful that any other action would work. Even an appeal to higher authority at the university might result in bad feelings that won't help you get your degree.
See if you can salvage good recommendations from this mess and find a way to move on. It isn't the end of the world. Many students change universities mid-stream.
I actually left one program in a somewhat similar situation: a dispute over a single answer on a prelim exam. I wound up at a better university with a much better advisor.