What you describe is not "extortion". You have a right to fee arbitration and you have a right to offer a lesser amount that the fee demanded.
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.
The law provides for fee arbitration if there is a billing dispute. The fee arbitration is mandatory on the attorney if the client requests it. The arbitration can be binding or non-binding.
That the attorney "feels" it is extortion is irrelevant. Whether you are right to withhold a portion or all of the fee is up to the fee arbitrators, unless the two of you settle.
If you threaten to report him to the Bar unless he lowers your bill, that would be extortion.
What you described here is not extortion. However, it might not be terribly effective to try to negotiate if the attorney isn't interested in lowering his bill. Your choices are to pay the full amount, arbitrate or sue for breach of contract.
Negotiation only works when both sides are interested. It doesn't appear that is the case here. Good luck!
This is legal information only and not meant to provide legal advice. Many issues that seem straightforward at first are often complicated by facts not revealed in a hypothetical posed by a member of the public. You should always consult directly with your attorney in order to ensure the issue is thoroughly discussed and that the proper course of action is taken.