I'm thinking a huge dragon head (like 3 meters long or so) with a wide open mouth, obviously with details like teeth and tongue. The bottom of the mouth could be used a bit like an air bed, flat enough to rest on. The mouth would be held open by a wedge-shaped chamber at the rear, if that is deflated the mouth closes (obviously without any force) for a 360° squeak. Maybe some pockets on the upper part that you could place weights into for a bit more squish?

Sorry, no 3d model, not feeling up to it right now.