Looking at the top picture, it appears that if the flywheel is rotated 45 degrees clockwise the beam will be roughly horizontal and the valve will be roughly at the mid-point of its travel.
This suggests the eccentric is about 90-degrees out from the correct position.
The starting point should be to have the valve at approximately maximum travel one way or the other when the piston is at its mid point (beam horizontal). The engine should then run and the eccentric can be adjusted to get the best result.
You are aiming for the valve to open just as the piston approaches TDC, whatever type of steam engine it is.
The double spring was probably needed to to stop the large rotary valve lifting and leaking with steam pressure applied.
Neil