Disclaimer: I know nothing about driving.
But, I'm thinking, OP that your noseband problem might be because the noseband is supposed to go inside the cheek straps, not around the cheek pieces like it is in your pictures... Maybe that would make it small enough?
At least, the cheekpieces are meant to be on the outside for non-driving horse bridles and I assume it's the same with driving...
Your girl is ADORABLE! :)
Fabio - 13 year old Arab/QH gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.