As far as I recall the local municipalities can enact laws that are not more stringent than state laws. There fore I believe both laws would apply as only judges and court officials with written permission can carry. And all others (LEO and such) can without permission. So the local law does not place restrictions on state law.
However the issue would be the actual issuance of this "written permission" does it happen? Probably not.
Also it statesThe way I read that is that ANYTIME someone enters and then leaves a restricted area they must re obtain that permission, theoretically at least. This would be a cumbersome and burdensome task, although it would be worth it....who, before entering the restricted area, directly and promptly proceeds to the court administrator or the administrator’s designee and obtains written permission to possess the firearm.
Just my opinion though...