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You could keep the current build using pulleys. cable and a cam, then equalize with weight. It is possible to build it so it moves with a pound of force and won't slam down when you release it.
You need a cam because the force needed to lift the door increases as the door goes higher. And it needs to compensate for the changing angle from the cable to where it attaches at bottom of the door.
But you gotta find someone to draw the cam for you...
It is neat that math can work around such a stupid design - how did you think it would work?
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