I'm not really an expert, but I'll say what I know. You probably know a majority of these game play mechanics by now, but I shall mention them for the sake of completion.
I don't think this game was made with the intention of grinding. Notice the pittance of experience you get from random encounters even when entering a new block. And then you get massive experience after a boss fight. I think you level by fighting bosses.
Think of it this way: levels only increase your stats incrementally at a very unnoticeable rate; just like real life. The only really useful thing level ups do for you is unlock new inventory at the shops every so often, and the ability to fuse higher level persona.
The really useful thing random battles give you is money and fusion materials. With all of the persona's you can acquire up to that point (including fusion), you can always beat in-game bosses (I haven't beaten the Monad block yet) by having the proper persona and weapon. I know you beat DDS, so you have to know how to keep a good elemental spread in your party by now. You just need to fuse the strongest set of persona using the available fusion materials.
If you insist on grinding though, the best choice would be on a night before a full moon (status automatically gets set to normal on a full moon night). Advance as far as you can until you get tired, then return to ground floor to ditch your party (it's mandatory), recover, and then level up the main character on a lower level run through. Logically, you pick the highest level where you feel you can survive indefinitely.
The experience will be as good as it gets (read: low), but at least you'll get money, and plenty of personas to fuse and add new entries into your compendium. Also, you should try to completely explore each randomly generated floor. You might encounter a rare treasure chest with an advanced weapon or something.
I don't know anything about fatigue, but it's not something that really limits me anymore with this strategy.