I don't think float is going to work with this header. Because of how the wings work, the header has to be suspended by the springs in order for the wings to flex up or down. Hard to explain. Basically if you lift up one wing, the linkage causes the joint for that wing to move down. With the adapter frame on the ground, the header is going to be super heavy and the flex action is likely not to work very well.
You could, however, manually adjust the feederhouse to keep the adapter frame up off the ground. That would be rather tiring though! Just fix the cables; you'll be way happier with the header when its working as it was designed to work.