"The Cask of Amontillado" would lose its timelessness if it were narrated the day after. Revenge and revenge stories are dishes best served cold. You can't tell them hot.
If it happened the next morning, you would have to change the ending from...
For the half of a century no mortal has disturbed them.
In pace requiescat!
...to something like "For half a day nobody has disturbed them." And then I don't know the Latin phrase for, "May he rest until lunch" is, but it's not as good, is it?
To change a word is to diminish the shock the audience feels when they realize that the narrator is an old man! That this old, sadistic murderer can remember his gruesome act with perfect and eloquent detail! No, the story must be narrated by old Montressor. This man could be our grandpa, for heaven's sake! Creepy.
The murder is not the horror in this story. The fact that Montressor's crime has remained undiscovered is the not the horror in this story. The way the story is told is the horror. The way the narrator either remembered the actual crime in such detail or the way he completely fabricated it with such detail is utterly horrifying. I don't know what's worse. Either way it shows the intensity for retribution Montressor must have felt. For what? What could Fortunato have said or done to make Montressor relish in revenge for over 50 years? This is the irony that must be preserved.
Do not disturb the framing of the story: May it rest in peace.