internal overload is usually caused by compressor getting too hot and that takes longer than 1 minute. Your low pressure switch will cause unit to shutdown as you explained. Quick way to check that is check for 24 volts across the low pressure switch. It will be 0 if all is good. It will be 24V it the low pressure switch opens. of course you will see 0 until the unit shuts down and the contactor plunger pops out then at the exact same time you will see 24 V at your meter.