I understand, though I doubt that such a lawsuit would ever succeed despite spending at least tens of thousands of dollars. You could try submitting a legal document with your application that would acknowledge HPD's legal and financial liability should they deny you a license and you suffer any negative effect in any circumstance where you might have avoided those negative consequences had you been granted a license and carrying legally. Of course they won't sign it, nor will they acknowledge that they refused to sign it. The other possibility is that if you or your family are ever subject to criminal assault or attempted murder you could ask the criminal to stop while you ask the cops if they could NOW issue you a license as you find yourself in "an exceptional circumstance". The whole charade disgusts me and makes me sick. 
There is a law to cover
"HPD's legal and financial liability should they deny you a license and you suffer any negative effect in any circumstance where you might have avoided those negative consequences had you been granted a license and carrying legally".
it is this -
Title 18 U.S. Code § 242 - Deprivation of rights under color of law
Whoever, under color of any law, statute, ordinance, regulation, or custom, willfully subjects any person in any State, Territory, Commonwealth, Possession, or District to the deprivation of any rights, privileges, or immunities secured or protected by the Constitution or laws of the United States, or to different punishments, pains, or penalties, on account of such person being an alien, or by reason of his color, or race, than are prescribed for the punishment of citizens, shall be fined under this title or imprisoned not more than one year, or both; and if bodily injury results from the acts committed in violation of this section or if such acts include the use, attempted use, or threatened use of a dangerous weapon, explosives, or fire, shall be fined under this title or imprisoned not more than ten years, or both; and if death results from the acts committed in violation of this section or if such acts include kidnapping or an attempt to kidnap, aggravated sexual abuse, or an attempt to commit aggravated sexual abuse, or an attempt to kill, shall be fined under this title, or imprisoned for any term of years or for life, or both, or may be sentenced to death.
Our local problem is finding a lawyer to help us prosecute this "Qui Tam" in a federal court,
when we are denied. Arbitrary, conceal carry permit denial is clearly a federal crime.