The problem here is not so much void ordinances, although there’s a bit of that, but the concealed carry licensing system. The law says they must issue or deny within 14 days, for instance, but there’s no penalty if they don’t, only the ability for the applicant to sue them in district court.
Are you saying municipalities are responsible for issuing licenses? If state has exclusive legal authority over weapons matters, such a policy would seem odd. Nonetheless, if the issue is that municipalities have the manpower to do the background checks and the state doesn't, a remedy would be to provide that applications get sent to the state which logs them and forwards them to the municipalities, which are required to notify the state of the result. Someone who is neither accepted nor denied within 14 days could inquire with the state the status of their application. Someone whose license hasn't been denied within 14 days would be deemed to have been granted one, at least until such time as the person is served notice of denial.