You can mix and match GC barding pieces, it just requires planning. If you say wear the full Lominsan Crested barding set and never ever take it off, it will persist between GC transfers. If you take a piece off at any point it'll be unavailable until you switch back to Limsa. You could have like Maelstrom head, Uldah body, whatever feet.
Major barding difference besides flag is the shape of the headpiece on the Crested set, of which Limsa's blade horn is superior.