Belly Bulge Test file (Patreon)

There's a skinrwap modifier with the rpoject option to make the deformation when the object moves. (just hide that object in render so it won't be visible)

And also really important thing: remember to make a shape key that smoothes the belly button until it dissapears. or it will probabbly make the mesh explode in that part with the skinnwrap modifier.