Just in case anybody comes to this thread looking for an off-the-shelf solution, there is an automated button pusher from Switchbot which has a manufacturer-offered smartthings integration and works quite well. I’ve written about them before. But at $30 per button pusher plus the required mini hub it would be more expensive than most of the DIY approaches. As always, choice is good. 
2020 Switchbot Review ( robot button pusher), integration through IFTTT or new V3 app
