I think Jan 31 is fine. Some people would say more, some would say less, but in the end it's 3 months....
Rather than adding the card and explaining it all, is there any way that you could buy more of the paper on which it's being printed (and if you're printing on cardstock, see if they have a regular text weight in the same style so it's thin)? If so, I'd just print the new date, and cut it out as small as you can and glue it on over the old date. (Even better if it's on white and you can just use a regular white label) That way you don't have to explain it, etc.
Good luck!