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So does anyone have some ideas about how we can have a cooperative variant?
Some things that can to mind, borrowing from some of the other variants.
1. Use blocking imps like for 2-player (and solo variant)
2. No auction. Use the 'no planning phase + fixed turn order' variant.
3. Food tokens do not run out. Replace when needed as per the 'Friendly Action Space' variant.
Would this be enough?
What would the winning condition be? Maximizing combined score? Anyway to lose the game? Having a score less than x?
I would do coop scoring as "the group's score is the lowest score among the players". So you only do well if everyone does well.
(I don't remember the other variants you mentioned, so can't comment. Keeping food limited seems like an essential part of the challenge, so I'm not sure I would refill food.)
I honestly think that this wouldn't need to be a varian, it would need to be a new game, based around the ideas found in Dungeon Petz.
I think one winning condition might be that you have to get a certain number of petz sold and taken care of.
I think the Dungeon Petz 'end of round minigame' (where you take care of the petz) is a really interesting springboard for a new game though and it might be worth exploring it.