You're asking for information that varies by evaluator, for a specialty exam where the attorney makes about $2-$6k per case before expenses.
"What is the going rate for an exam that varies by person, location?" That's like asking, "What do women across all ages, education, religions, etc want in a man?"
Shot in the dark: $300 for exam and report with zero testing. Maybe $500. Office full of people acting up because their claim did not go well in round one. Driving away your normal patients. People returning to your office to yell. I wouldn't do it.