I had this problem, and eventually did as advised, i.e. turned off carrying food. They still can carry alcohol, and it seems it's OK. But what I did additionally was designating every of these affected item to dump. Eventually, after two or three years, all items were thrown to the quantum stockpile, with cleared ownership. Only exception were items owned by one particular dwarf, Urist McHoarder, and it was food only. I don't know why, he's still alive. He's also only the one military dwarf (out of 29) who still keeps some owned food in his coffer. All others cleared their possessions and keep empty coffers, they use only their cabinets. I think it may be related to his civilian job, that is mining. He is from my second wave, other miners-soldiers (or woodcutters-soldiers) were recruited after I turned off carrying of food. He was recruited before.
I think that only owners of these items were dumping them, that's why it took so long - they were in military, and seldom had time for other duties. Anyway, I speeded up cleaning by moving other items from affected stockpiles, sealing off these stockpiles (with mostly food), disabling refrigeration and waiting off.
EDIT: Oh, and I also allowed them all to keep their uniforms when off-duty. Maybe that helped with alcohol, since they don't drop their flasks and waterskins everywhere as before.