At the end of the 19th century, the word «hangover» meant «hangover thing that has survived until today. «Drank so much that even today remains» appeared somewhat later.
The morning after a large-scale feast is called the morning after (spoken version). Sleep off/away is sleep it off, sleep, get over it. A cure for hangover informally referred to as the fur of the dog. Once it was believed that the only remedy for the bite of a mad dog, to take their drinks with a tuft of thair fur. Fire with fire, so to speak.