Circuit to turn microcontroller on when reed switch state changes (to monitor door lock state)
There's no way to test the state of a reed switch without attempting to pass current through it. If you don't want to pass current through a closed switch continuously, then you need to have some process that periodically checks the state of the switch by applying power to it.


  I've also though about maybe having the ESP8266 in a deepsleep-wake cycle every 5 mins or so and just reporting the state of the reed switch ...


You're on the right track. If the ESP8266 itself consumes too much energy doing this, then consider using a much lower-power "auxiliary" MCU to do this testing, which can then apply power to the ESP8266 only when it's necessary to send a message.