I was able to create a new view within an existing nested view, as described by Patric Boström in the comments for this issue:
The new view is inserted correctly and works fine. However, this seems to have broken other nested views as they are no longer found (HTTP error 404). I have attached the error message written in jenkins the log file.
It seems that when I get the config.xml via the REST api, it is missing the "owner" nodes. This can be seen by comparing get_config.xml (received via the REST api) and partial_config.xml (an extract from the jenkins config.xml file).
As a work around, it is possible to insert them before updating the view.