I've only "ran out" of LP once. I haver an outdoor kitchen and and a grill connection on the rear bumper. I connected the full tanks, then connected the grill and turned on all the burners. It didn't take long to purge all the air out of the main line. Each branch off the main still had to be purged, i.e. the fridge, water heater, and furnace. I would turn on the burners (all of them) on the stovetop then try the furnace. That should purge the gas the gas line fairly quickly.
2012 Laredo 303 TG
2010 F250 LT Super Cab, long bed, 4X4, 6.4 Turbo Diesel