Well below is a circuit that might work. It switches the power to the safe electronics via a P-channel mosfet. The mosfet is turned on when the DS3231 alarm triggers and /INT goes low. That happens once a month, and the Pro Mini also turns on.
The Mini first checks its EEPROM to see if 12 months has elapsed. If not, it writes to the next EEPROM byte or word to record how much time has elapsed. Then it brings D2 and D3 high, which keeps the power on and provides Vcc power to the DS3231. Then it clears the alarm and sets up a new one for a month later, all using the I2C lines. When all of that is done and /INT has gone back high, it turns off D3 to return the RTC to coin cell power, then turns off D2 which turns off its own power and the safe electronics. This setup does enable the safe every month, for only for a second or two.
If the EEPROM data says 12 months have now elapsed, the Mini does nothing. It just goes into Power-Down sleep, which should reduce its current draw to the regulator's no-load idle current. The DS3231 alarm will not be cleared, and it will continue to run off the coin battery. Power will stay on indefinitely.
To start a new time lock, the EEPROM would all have to be re-initialized, and the DS3231 would have to be programmed with new alarm settings.
I should have included a manual switch that bypasses all this stuff and just turns on the power to the safe electronics. That's something you would want to have.
I should say that there is another RTC chip, the M41T81, which does let you include the year in the alarm settings. But I've found only one module using it, and it's over $10 plus shipping. You could do your own, but you'd need a coin cell holder and a crystal and some board to put it on. If you went that way, the Pro Mini and NPN transistor wouldn't be needed, at least not inside the safe. You would still need a way to set up a new time lock.