Well, the simple solution available right now is a new membrane for £20. One of those is certainly better than trying to breathe life into the failing one
The A500 keyboard has exactly the same type of membrane and connector so I don't think that in itself is the problem. It just doesn't get moved around in that configuration. Maybe an adapter PCB of some kind could be made so that the membrane on the A600 is immobilized, something similar to what Daedalus was talking about earlier.