Should I grind until last minute for a story palace, or clear it as soon as I can?

I'm in the first palace, and I get 2 weeks to beat it.

I'm close to clearing it on Friday of the first week, but IDK if I should push now to clear it or grind the mobs for levels/money before clearing it on the eleventh hour.

The story so far seems to hint at the fact that when I clear it, the palace would be gone and so the mobs in it would, I guess, not be accessible anymore.

So in most cases, is it preferable to clear the story palace as soon as possible, or is it better to wait, grind what you can before clearing it?