Yes, these groups have some activities that do not fall under lobbying. They are actually doing lobbying that could be described as indirect, meaning that they make the media aware and then the media might make public office holders aware. Sometimes, these groups communicate with public office holders. I am thinking of Friends of Science, for example, which has been very active. If that's the case and if that needs to be registered in the registry, it would be very easy to simply add a line or a field for those groups to specify what their major sources of funding are.
That would not fully lift the veil on the issue, but it would at least lift some of it, making some of the activities of these groups transparent, including lobbying. In a nutshell, this is a simple measure that would make it possible to partially lift the veil.