Having found that Coco Coir is not at all the same as Coco Pith, I am now stuffing the gap between the medium and the fabric pot with lots of Coir fiber.
This seems to work well, keeping stuff on top from falling, and generally helping the medium stay in contact with the fabric.
As for damage to the root system during moving, this is a hazard of soft pots, hard pots do not allow nearly as much air, but they do a great job of protecting the root system from harm.
Be gentle while moving soft pots, drag them around if you can.