How to customize Schema.org at node level?
As I understand your question, you would like to be able to override the Schema.org types per each node separately.

This is not possible at least out of the box. You would have to write custom code to display a tab on each node form, store it somewhere and then load it when the node is about to be viewed.

This is because content types are generally used for storing the content of the same kind. For example: an article, a blog post, a static page, a webform and so on. This means that all nodes of certain type will need the same Schema.org declarations, and that's why it was implemented this way.

You are probably storing different kinds of nodes using one "generic" content type. This is not the most common use case. Unless you have strong reasons for doing this, I suggest migrating the content to separate content types. It will benefit you in case you want to use other similar modules as well, such as Metatag.

Hope I managed to explain it.