Hi, thanks very much for this explanation. Boy, was I tearing my hair out; now I'm an expert!!
I do have a couple of comments / clarifications which may be useful:
The most important thing (TWIST IN THE RIGHT DIRECTION): when tightening spiral / spring, prop window open with a stick (or whatever-- prop it most of the way open); IF THE SPIRAL HAS COME OUT OF THE TUBE: push spiral up, gently, into tube, don't force, let it twist the way it wants to twist // stop when about 2-4" of the spiral is still showing below bottom of upper sash & tube; then, hook the tensioner tool to the end of the spiral, and, counter-intuitively, twist in the same direction it was going in-- I think this is counterclockwise, if your head were under the window looking up. I say counter-intuitively, because I kept trying to tension it by twisting in the wrong way-- you know it's wrong if it would want to shoot the spiral out towards the floor, if you let go.
You are screwing the spiral up further into the tube, with the hook-- so there is pressure pulling it up, not pushing it down? that will allow the "t" nib at the end of the spiral to latch onto the holder on the bottom of the sash, and the pressure keeps it there. But you only twist 4-8 times (still experimenting.)
Then you jimmy the "t" nib into the slot at the end of the metal piece on the bottom of the sash, and jimmy the tool end to release it. The tension on the spiral holds it ( the "t" ) in place. This can be difficult or easy. On one of mine, I had to release the screws holding the plate to the bottom of the sash, & let / force the plate to drop a little to expose the catch for the "t." Then, once the t was in place and the hook tool released, I could screw the screws back in. this may have been because the wood was funky and I should have consolidated it better, or the old plate was a little bent.
Then, you can release the stick holding the upper sash, and the window should stay. When you push it down, the more you go down, the more resistance you will feel, as the spiral / spring tensions and wants to pull the window up.
What a lovely design -- when it works!