"2) The results are racially discriminatory. Minorities fail it at a higher rate. Strict scrutiny, not rational basis, Sir. The Bars will not release the failure rates by sex and age, despite any sunshine law. Intermediate scrutiny may also apply if enjoined for the data. You will be surprised to learn that law students have unanimously panned such Federal court action, even just discovery. I would be curious to know the opinions of the law students. They want to take and pass this exam. "
Possibly...Also you might have better luck with an argument based on cost and lack of ABA support for accrediting bar preparation programs. The dissent in the Montana supreme court brought that point up...the appelant against ABA only lost 4-3. Also an Americans Disabilities Act ( argument might be made for the ABAs refusal to accredit online law schools which prevents people who cannot attend regular law classes due to physical or psychological disability from practicing law.
"3) Its structure stems from Alexander of Hales, a 13th Century friar. It violates the First Amendment Establishment Clause. "
Universities were first established by church based organizations...this argument is irrelevant
"4) It lacks modern psychometric competence. It was advanced in the 13th Century, to its credit. What are its 5 forms of reliability? How was it validated (a technical statistical term, not a philosophical one)? One IQ test, the most validated, and powerfully predictive test of all time, with 10,000 validation studies itself, was banned because of racially disparate results. "
The bar exam doesnt have to be competent as long as it is equally incompetent for everyone.

"7) The Separation of Powers..."
Youd have better luck with the federal courts and an argument based on restraint of trade and the issue
of admission to the federal courts being effectively set by state legislatures and the ABA instead of congress.