SomethingClever:
The Mini needs to be powered from the Feather, but as far as I know that should not be a problem?
The Mini power input is 7-9V. How are you connecting it to the Feather to get a voltage in that range?
SomethingClever:
Would it be feasible to use a second controller, e.g. a Pro Mini to handle the data logging and then communicate with it via I2C?
Sure why not? There's an example around here on connecting to Arduinos via I2C.