First, I'd recommend instead doing those two playthroughs on the same file, because the postgame requires you to complete and use all eight characters. Naturally, because your main character is locked in your party until you complete their full story, you won't be able to do a concurrent 4 x 4 run, but you'd be able to do your initial four, then the next four after completing theirs.
Second, as to grinding: it isn't necessary. Recommended levels and danger levels are less indicative of what level you should be, and more indicative of what your equipment should be like, or if you're using the right strategy. Equipment far exceeds level ups in stat gains. If you did a run of 4 characters after completing the other 4, your second group would actually be almost as powerful with the endgame equipment, just having less HP and fewer abilities/passives from JP accruement.
As long as you unlock subjobs after/during CH1, and explore some optional dungeons, you'll be more than keeping up with your first group's suggested levels, anyway.