Hi. I don't do iOS management, but I don't think this is possible, meaning, its not part of the MDM spec to be able to group iOS apps into folders through any kind of configuration profile or otherwise. Not outside of using the methods you already mentioned.
Someone please correct me if I'm wrong though.
@mm2270 is correct. You cannot organize apps into folders using the JSS.
In configurator I believe you can backup an iOS device with apps installed and in folders then restore the backup. The apps will get sent over with configurator (since backups don't store apps) and SHOULD go into the folders you defined.
With the release of iOS 9.3, Apple added a new Configuration Profile to customize the Home Screen Layout of apps, including organizing within folders. Casper Suite allows you to build and deploy this Home Screen Layout profile to define which apps appear on which pages, or in which folders, on your iOS devices.