The most efficient thing is to get a new attorney if the case is going on.
You have a right to mandatory fee arbitration under California State Bar rules.
You have a right to file a complaint with the State Bar.
Don't worry about the burden of proof.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.