The "primary source" Ryoko Kui used for the manga is Wizardry, which is surprisingly similar to AD&D. I'm musing abou writing some quick rules on Dungeon Meshi OSE Advanced. It would be mostly replacing "XP for gold" with "XP for having a balanced diet" using these principles:
1. you gain XP for killing monsters;
2. you only gain XP when you sleep 8 hours, and you don't gain XP for monsters you killed more than 24 hours ago;
3. at the end of the day you add a multiplier to the XP amount you gained according to how many nutrient groups you have eaten (proteins, vitamins, minerals, carbohydrates and fat) up to ×5.
Then you just need to decide which monsters have which nutrients and it's done!