I did something similar, starting off as CNJ and switching to ACN at lvl20. What I ended up doing was traveling to another area and used a combination of FATES, hunting logs, and small quest hubs (the lvl 10+ hubs will have their own quest chains if you haven't done them yet) to get my ACN to 20 and have them pick up my story quest line.

If you want to run the Limsa Lominsa or Ul'dah storylines, there is no way except to make a new character with a class starting in those cities.