Don't wait till then because it actually takes an extra day (or two) more than you think. Better to do it earlier but it doesn't have to be the very first day or anything.Should I be going to palaces as soon as they unlock, or should I be using that time to strengthen relationships and then trying to clear the palace on the very last day before the deadline?
Just remember to try to make it as far as you can until you're out of SP or HP before exiting since time doesn't advance until you exit. The worst thing you could do is spending eight days in a dungeon (for example) if you can do it in just two as that waists six days you could be doing other things.