JAL might let you choose check in, I even guess the would as you departure is the next day (technically speaking) but check will be requir the day you arrive.

The lounge will be more complicated, it is on the other side of immigration, you will need to be processed for leaving Japan to go airside. And then be escorted back to immigration to enter Japan again, entry and exit formalities are on separate floors. I would go for the land side option for showers if I was you. Or check if SQ has an arrival option in Narita.