i get around 45seconds of power time from the 4.5F cap when just running an RPi and around 20secs when running a HAT/ancillaries, the RPi3 can remain powered up until the voltage depletes from 5v to around 2.4v but shutdown is initiated within 1 second of power loss and full shutdown takes just 6se...

I am also in the middle of planning a cheap Pi car media player. About power management - software shutdown will not be enough to prevent battery drain. You will be left with 100mA, enough to prevent you from getting the car started after a week or so. My solution is (will be) a battery cutoff which...