The best source of food with satiation to weight ratio is at the arena in the CoC where you can trade for fried lizards with the ratlings. Fried bat is the the next best thing but anything else just isn't worth it. Cheap too. Rations from the starting town are only really good for getting across the wilderness to the CoC. Some corpse effects are lethal and can affect your stats in the long term, but a lot of them are useful for getting most of the resist in the game. If you have a character with Food Preservation it increases the chance of a killed monster to actually drop a corpse but it isn't THAT necessary, but still one of the better and useful skills to have compared to other skills like music (unless you are a bard that is).
Equipment that grants invisibility is very hard to find (and it speeds up hunger too), and you're best bet to be honest would be to get invisibility from pool drinking (which does not affect hunger), but that in itself is risky behavior and you would want to be be lucky and have fate smiles before you dry up the pools which are not that hard to find in the game. There is actually a dungeon in the game that has guaranteed pools.
For all the time I have put into this game I would throw a mental party in my head for when I finally do beat it.