First thought, use a roller micro-switch to monitor when the door starts to close.
Mount it inside, connect to dry contact sensor etc. etc.
Roller Switch
Second thought, modify Sonoff SNZB-04 to monitor when door closes.
Not so much modify as build a mount. A mount that allows the door to lift the magnet close enough to activate the sensor when at it's top position, and drop away as it closes.
An old Tic Tac container and some standoffs bravely volunteered to "prototype" 
the concept.
