Adding json as params to shortcode

You could create a shortcode with only one attribute and that attribute could be the ID of a custom post type or the name of a site option:

[example id="123"]

Multiple instances of the framework

If you need to have multiple instances of that js framework with different attributes, then you could create a custom post type and use custom fields (meta-data) to save the attributes of each instance. And on the shortcode you would just read the custom fields of the post with that ID.

Only one instance of the framework

If you only need one instance, you could save those attributes as an array inside options database using Options API, and the ID would be the option name. And on the shortcode you would get_option by that ID.