1.0 players however basically were given ARR for free though - which includes the CE (1.0 CE owners automatically got the ARR CE items, including the Fat Chocobo mount and wind up moogle minion). I know this for a fact because I own the 1.0 CE, was able to download ARR for free and was automatically sent the ARR CE items at the relevant times.

These were sent to 1.0 CE players via the Moogle Delivery Service, which sadly has a limit on how many messages it can hold, including system messages like item rewards. It's possible you might have too many system messages stored and thus just need to clear these out before you can receive the relevant one with the Fat Chocobo mount and moogle minion.