After the level 10 class quest on your starting class (and then the story quest that gives you airship access), your starting class makes no difference to anything else in the game. Stop doing quests on CNJ. Switch to another class and level it to 13 via hunting logs, leves, and FATEs. It'll be just like you started on that class and leveled CNJ to 13 on the side. If the class you want to switch to is in another city, you'll have to make your way through the main story at least until you unlock the airship (around level 15) and travel to that city to unlock the class at its guild.

I'd advise you to stop doing side quests entirely on both CNJ and the class you want to switch to. Stick to the main story quests, hunting logs, a few fates/leves/dungeon runs/guildhests when you need them to pick up a level or three to qualify for the next main story quest. That's enough to level at a decent pace, and it'll leave side quests for future classes you might want to level, which won't have the main story quests to help them along.