I would not worry about the dog carrying the pillow. I feel like this is a relic of old-school training. If the dog is biting nicely on the helper then I would just accept that. Forcing the dog to "cradle" can sap some of the fun out of it for the dog and ultimately may affect the relationship.
Check out my website dedicated to IPO/Schutzhund:
To view links or images in signatures your post count must be 10 or greater. You currently have 0 posts.