I would like to preface this by saying I'm fine with the food update as it is, however seeing as how food is the biggest criticism the new update is facing, I feel like a cooking skill wouldn't be a bad idea. There certainly are a lot of skills in this game, so adding one more couldn't hurt.
It could make it so that if food is cooked, it adds experience to the cooking skill, which would make it so that players get bigger boosts from meals. Could tailor it in a way so that cooking low-tier foods provide little exp to the cooking skill, while cooking top-tier foods adds a lot of exp. It doesn't have to be something massive or get close to pre-nerfed foods, but it certainly would be able to help out the players who are upset about the food changes.
In terms of inventorying these kinds of items, I would imagine the best approach would be for similar foods to take the average of the benefits that they provide in the stack. Not 100% sure, but my best guess.
I feel like with the initial comment from the devs saying that they wanted to make the food selections interesting, this would only add to the variety the game has to offer. For solo players, they can, in time, get close to the old food stats that they crave, and for the co-op servers, you could have someone focus on being a chef, so that the team relies on him/her to provide meals for the party when they need it.