Hey maybe you could take your cat to the vet for a cortisone shot since a lot of people say allergies. That really seemed to work for my neighbor who has a little Russian Blue who would get everyone wet when he was snuggling on our laps.
They drool because their saliva glands are controlled by their hair follicles. When you move a follicle by petting, they start to drool from the interaction. It is sort of the same as Pavlo's dog experiment.