What is needed is a way to stop the wobble caused by acceleration of the effector, and possibly the drag of the extrusion material. Two sides of a parallelogram stay parallel even if the angle with the other two sides changes. So, how about we use two strings from each support so the parallelogram is in the vertical plane? Well, that means three attachment points higher and three lower to the effector. Strings can get shorter by folding up a bit, but are (relatively) inextensible. So the parallelograms should be stable enough. Mmm...ok at the effector, but what about the motors?
Well, each motor now needs to wind in and out two strings at the same rate. One motor can handle that easily. Each spare string needs to be kept clear of the other, and still have an accumulator, and that seems to be a simple piece of engineering, too.
There is no change to the kinematics needed, so software is unaffected.
This whole idea was the result of just thinking further about a question asked by @Florian Festi in a reply to one of my comments on Someone please build a parallel cable robot over in https://hackaday.io/project/11583-odrive-high-performance-motor-control. Now, Florian might be disappointed that I have not reverted to kinematics more like a delta printer, but Florian should be pleased that I have been inspired to think further about stability of this printer. Thanks Florian, for making me think about delta printers.
Oh, yeah, and if this idea doesn't work, it is nothing to do with Florian.