Hi,
thanks for your post, and sorry for the trouble.
Sorry, it’s not directly possible to import from sources that are protected by a login or that require authorization. That’s because WordPress does not offer native features for this.
My recommendation would be to use a custom PHP wrapper script, kind of like a “man in the middle”. This would receive the import request from TablePress, and send out the authorized request to your JSON feed API. You could then also use that script to alter the JSON return format to a two-dimensional array.
Regards,
Tobias