I think your struggle with this model is because you assumed that the angel of rotation of both levers is identical. Because the levers differ in length the structure is not a regular parallelogram (equal opposite sides). Hence the rotation in every corner is dissimilar.
As a demo, in 2DOF_Lift 000.3dm (765.1 KB) both levers are equally long, hence the parallelogram is regular. This makes your initial setup (in which both levers are “driver”) feasible. To ‘close’ the parallelogram I use an auxiliary point and line. This technique is illustrated in this video http://bongo.rhino3d.com/video/the-conception-of-an-ik-chain-a-scissor-arm
I rather use a point and a line than 2 points – it bypasses accuracy in positioning.
But for you irregular parallelogram an IK structure with only one “driver” is needed (like in Joshua’s solution). More easy to understand (and to build) is the linear structure of the IK chain I used in 2DOF_Lift 001.3dm (750.3 KB)
The use of a “keep pivot location the same’ constraint makes use of auxiliary objects unnecessary.