A well screen system includes upstream and downstream screen assemblies arranged along an axis. The assemblies each have first and second transport tubes. A first packing tube is connected to the first transport tube by first adapter and has an uppermost nozzle axially spaced from the first adapter by a first effective packing tube length. A second packing tube is connected to the second transport tube by a second adapter and has an uppermost nozzle axially spaced from the second adapter by a second effective packing tube length different than the first effective packing tube length. The downstream screen assembly second transport tube is connected to the upstream screen assembly first transport tube to alternate the effective packing tube lengths of packing tube uppermost nozzles along the screen system. Methods of making well screen systems and methods of gravel packing well screen systems are also disclosed.