Food for thought from someone with similar living arrangements:
Change the lockset on one of your closets from an interior non-locking one to a keyed entry lock. Voila, your locking gun cabinet.
Self-install a SimpliSafe wireless alarm system in your apartment. Monitored by SimpliSafe who will communicate directly with your local police dispatch in the event of a break-in. Your landlord (and G-d knows who else) already has a key to your new apartment.
The SimpiSafe system has a camera that will record (to the cloud) all entry activity. They also have a 'silent alarm' entry sensor that will be triggered when your gun closet is opened unless you specifically bypass it.
Very reasonably priced. The system communicates with them via wifi and has a cellular backup.
It's the best $36 a month I spend for peace of mind. And there are discount codes available in their ads on most conservative radio and tv stations. I can also do a referral to you. PM me if you want.