In the meantime, a 99designs for people with time, knitting needles and sewing machines seems like a lovely idea, and easy to achieve.
The little brats (well, my own), are already the center of enough attention. If they want to make their own stories, they should go outside, play and invent them themselves.
It's obviously not something you can send off to China and press the button on an assembly line. Some things just can't be mass produced, and we should be grateful for that.
Franchising perhaps? Quality control would be an issue once you start farming the job out like that, but it would be a good way to better cover international markets. They could keep the designing local to the current HQ, hiring designer types there to supply demand and farm out the physical work.
Though I suspect a project like this might be a personal one, they they don't particularly want to scale massively.
That way customers from any country go to the same place (saving each member of the co-op on advertising budget/time) but get the work done by someone more local to them so hopefully pay less due to local delivery and lack of customs charges.
You migth find many peopel who are capable of making something like that from a pattern but maybe no capable/comfortable making a good pattern from the kids' designs - there would be a value add" there having that stage done for you. I know a few people who make things (and make them well) as a hobby but who do not make their own designs - I could imagine one or two of them being interested in getting involved at that level just to make the hobby pay for some of itself.
Obviously any controlling company would have to give some quality assurance to the customer, which would be part of how they justify their cut (as well as providing the design stage if they are) though could be a bit of a nightmare. This assurance might be why people go to this hypothetical cooperative rather than one of the smaller groups (or individuals) that try under-cutting them.
The work is done on an individual basis by an artist who not only takes great pains to interpret what the child has drawn, but also above and beyond to transform it into a personalized, and near perfect, piece of art.
Just ask any offshore worker to reinterpret a set of well-documented requirements and you'll see what I mean.
Also, the potential for building brands seems pretty spectacular. Stuffed toy is just one step, you could add stories, games, episodes...this could be to disney what 99designs is to graphic designers :)