Anyway, Zell should be in your party so you can activate the machine w/o using any steampoints or whatever and that way you don’t have to go up again.
To get down, I think you either need to use 2 or 4 points on the first floor (try 2 to start with, if it doesn’t work reset and use 4). Then 1-2 to get to the next floor (again, try 1 first, then 2). In the next floor there should be a room with reserve steam units, so you can go in there and you get 7 more units. Then just keep using as few as possible to get down, and you should have 10 when you get to the bottom, which is just enough. 🙂