Currently, there is no way to tell the PlayDate (at least, using public APIs) "hey, drop what you are doing and run this .PDX for 30 seconds". But I am pretty sure that developing such a tool is a realistic goal.
The sdk contains a tool to do this (the "start a new pdx" part) , called 'pdutil'. I use it regularly to send new builds of my game straight to playdate (from the terminal) without going through the simulator
Be aware that using the Mirror app has significant impact on performance though. Gravity Express runs at 30fps on hardware, 22 fps when using Mirror.