That would actually be a bad idea ... because that Great chef would get the settled spec bonuses from Representation and Sistine.
Good point. How about forget the specialist, and make the caravan unit create a special building instead (like e.g. great-scientist builds academy). This special building, the "Restaurant", adds a few food (like Baray adds +1PT, but more).
Hey presto ... etc. (this time no breakage of settled spec boni )
Again not really sharing food but at least transferring resources from one city to another. Could even have an equivalent one that ferries some over to help with those 1-tile island cities.