http://le.utah.gov/code/TITLE53/htm/53_05_070400.htm
53-5-704. Bureau duties -- Permit to carry concealed firearm -- Certification for concealed firearms instructor -- Requirements for issuance -- Violation -- Denial, suspension, or revocation -- Appeal procedure.
(1) (a) The bureau shall issue a permit to carry a concealed firearm for lawful self defense to an applicant who is 21 years of age or older within 60 days after receiving an application, unless the bureau finds proof that the applicant does not meet the qualifications set forth in Subsection (2).
(b) The permit is valid throughout the state for five years, without restriction, except as otherwise provided by Section 53-5-710.
(c) The provisions of Subsections 76-10-504(1) and (2), and Section 76-10-505 do not apply to a person issued a permit under Subsection (1)(a).
(d) Subsection (4)(a) does not apply to a nonresident:
(i) active duty service member, who present to the bureau orders requiring the active duty service member to report for duty in this state; or
(ii) an active duty service member's spouse, stationed with the active duty service member, who presents to the bureau the active duty service member's orders requiring the service member to report for duty in this state.
(2) (a) The bureau may deny, suspend, or revoke a concealed firearm permit if the applicant or permit holder:
(i) has been or is convicted of a felony;
(ii) has been or is convicted of a crime of violence;
(iii) has been or is convicted of an offense involving the use of alcohol;
(iv) has been or is convicted of an offense involving the unlawful use of narcotics or other controlled substances;
(v) has been or is convicted of an offense involving moral turpitude;
(vi) has been or is convicted of an offense involving domestic violence;
(vii) has been or is adjudicated by a state or federal court as mentally incompetent, unless the adjudication has been withdrawn or reversed; and
(viii) is not qualified to purchase and possess a firearm pursuant to Section 76-10-503 and federal law.
(b) In determining whether an applicant or permit holder meets the qualifications set forth in Subsection (2)(a), the bureau shall consider mitigating circumstances.
I did a google scholar search buy came up with only 1 case and it had nothing to do with your denial.
But google scholar only covers appellate and supreme court decisions .. there may be a slew of lower court and administrative cases to guide you.
It looks like the denial is a "may" deny due to your criminal records. Trying to minimize the seriousness of the conviction is never a good idea. Clearly you turned down an Article 15 thinking that it was nothing that they would court martial you for and was wrong.
The law seems clear enough .. it is within the authority of the body to issue or deny your permit. Unless you can find some case law saying that your crime is not a reason not to issue, you have problems as you have a finding not in your favor right now.
You could include the argument that you have the right to possess so you should be able to bear (otherwise its only 1/2 of the 2nd amendment you can use). I would certainly include this as a legal argument. To preserve the issue at least.
Now if the issuing body thinks that they must deny then this would show that they did not exercise discretion at all ... and this would be a violation of your due process rights under common law. The process should be fair at least.
There is an appeal process. You may take that route if you wish.
You could always re-apply..I do not see a limit to the # of applications over time that you could file.
If you are looking for a magic bullet ~ there isn't one.