Upholster the baby chair - This is bear country

We were given this beauty almost one year ago by a friend whose baby has outgrown this piece of furniture for, say, five or six years. Right, I´m always in for second hand stuff but this padding is...well...special. And very yellow. And has a weird patchworky bear on it. Also, it would be impossible to get the fabric tidied up without using harsh chemicals because it has waited through winter down in the (not so clean) cellar.
So, currently, the little owlet is perching on a towel (and always knows where said towel is) but this is only a transitory solution since I´m already measuring up a new upholster for this seat. I´m using the grand mushroom fabric and the leftover lining/padding from the patchwork blanket I did in the winter. Having been aware of the seat´s condition I ordered some more lining back then to have it a handy as soon as the little owlet was fit enough to perch in this seat, thus effectively saving shipping costs with my fabric/patchwork supply dealer. Talk about planning and cost effectiveness:-D!
This is what that padding looks like in all its flattened glory: