Whenever you gain a level in Bravely Default, does your current job have a permanent impact on your stat growth as it did in Final Fantasy Tactics? If so, is there a way to level down and exploit this system as there was in FFT for crazy min-maxing?
I am going to say no. There is absolutely no way to level down so no seems like an even more appropriate answer. Since you do not have access to all jobs from the beginning it would only be detrimental to your late game builds. I personally did not notice a distinct difference in magical ability between my characters that were White/Black mage's upon level up compared to me Knight/Swordmaster whenever they switched classes.
As far as maxing your stats go I'm thinking best way is to master as many jobs possible while staying at lowest level possible in order to get the most bang for your buck with freelancers late bloomer ability. I could be wrong but I would think more levels to go with those % stat increases in each stat would add up to something. In my game I already have the growth egg and at start of chapter 3 all characters level 32/33 and basically just grinding JP for now so I will let you know how that works. After looking around the net it seems I was confused in how late bloomer works, so perhaps stat maxing is not possible in this game