I suppose the NY Park West postmaster/manager hasn't heard about this Express Mail thing where he/she could have gotten a resupply in a day from the Fulfillment Center or a larger NYC post office. Postmasters may be members of different street gangs, perhaps.
Every counter station has a lockable drawer that is large enough to hold many hundreds of panes each. Unless you don't trust the counter staff, who are immediately responsible for any loss? Registered mail is stored in lockable cages but those are on wheels if you also think an inside job is possible.
In a day and age when you can buy forgeries at deep discount, even "pretty" ones for wedding invitations, who is going to steal them?
The article has been updated. I see where the postmaster/manager finally discovered a telephone could be used to make calls and found some way of getting a supply. DHL, perhaps.