Hey, I love BITBBH too! I would say that for the bear you may struggle to find a fur long enough for him but if you have a larger budget you may be able to have a look at National Fiber Technology who make furs for the Henson Creature Shop! Here they are: https://www.nftech.com/
For Tutter I would say that he is made much like the head of Kermit with just the performers hand and arm inside of him to get the most expression out of him! If you feel like he needs a bit more shape to him you could add little pillows of stuffing into his belly/leg area!
Have fun making them!