re: But I just realized that the exporter needs an option to select between the three privacy levels or we could end up disclosing unlisted or private information:
One of the columns in the CSV export is “Visibility” which will be public, private or unlisted. You can use Excel to filter these accordingly. That said, the export will not have the visibility of the individual addresses, phone, email and such. Is that what you are asking to be exported?
re: Additionally, we’d like to be able to group the data by Family where the family record is exported above each set of family members with different field names.
Sorry, this is not possible. There is no way to order and group them like this. Not a perfect solution, but you could sort the CSV file in Excel by last name.