I agree with the previous poster. I've been doing CUL leves because 10,000 gil per HQ turnin is a lot of money. However, that 'repetitive stress injury' menuing is killer at least for the boredom. But each leve is like finishing a milestone in the weekly challenge log! I have to do it!

Maybe the solution is for the entire leve system to just go away. It was designed in 1.0 as a way for the game to have repeatable quests. But we have so many more types of repeatable quests now. Leves have cool lore with their weird stained glass cards and light-up countertops. But the devs clearly feel forced to make them and they make as few as possible each expansion.

If it's about EXP then GC turnins and the relatively new Cosmic Exploration have leves beat. The moon will level any DoH from 10-100 almost as fast as FSH levels during Ocean Fishing. If it's about achievements then just add "leves or Stellar Missions" to all of them. The moon is already exactly what the OP asked for - endlessly repeatable leves with "no reward".