Hello again!

Firstly your flowchart makes perfect sense... so no worries there!

I think as far as deepsleep is concerned, it is unfortunately NOT an option, because as I understand it, when the ESP8266 (Oaks brain) goes into deepSleep mode... the only thing running is a clock that wakes it up again - so it can't monitor pins for changes, etc. The only way I know you'd be able to pull that off would be to use another microcontroller (DigiSpark to keep it in the family?

) to do that actual door monitoring, and it wakes the Oak up to do the actual wifi/particle stuff. That would probably be the most power effecient route, but not the simplest.
However, it may be possible to use other sleep modes on the Oak to bring it's power consumption level down to a more practical level. I fiddled around with that on some other Oaks, so I'll see if I kept the code. Basically, you can shut down the wifi module when you don't need it, and can also have the CPU go into standby mode, and it can be woken up by a interrupt (pin change), and then you can restart the wifi, and send stuff as needed. I'll see if I can knock something up between now and Sunday.