I have not done a transit tour, but based on the layout of the airport: If your transit tour desk is airside, you have to follow transit signs and you will stay in the airport. You can then inquire at the desk about an earlier tour. Even if you have your BP for flight #2 , I'm sure they're going to make it very difficult when you try to go back in , the go out, then go back in later in the day with all the markings and stamps on it.

If your transit tour desk is landside, you cannot ask any airside facilities like the lounges or showers. You have to go directly outside through Arrivals. Then you could ask about your tour at that desk. There is a sauna in the basement of the airport that's currently under renovations but should be open again this month.

Again, on January 18, the airport itself will COMPLETELY change as Terminal 2 is opening. Things will surely be shifting over time (locations of lounges, etc.) but rules should still stay the same.

If you really want to do it yourself, a day in Seoul can easily be done by yourself on your own time.