Hi Rob!
If I understand correctly you want to hide those settings (terms and custom fields) on the front end, which are not related to the selected custom post type.
If this is the case, then it’s not possible. This is a very specific problem, I don’t think I would be able to integrate as a feature. I think this would be only possible with heavy plugin modifications only.
I would rather suggest to create separate search instances for each custom post type, if you have many terms and many different custom fields related to them.