There doesn't seem to be any way within the Machform admin to import entries as you have already identified, and the Import/Export toos is concerned with the form structure, rather than the actual Entry records.
The import is definitely the one thing that's missing from this application.
Possibly you can get Appnitro support to do this. If you can export the database to a *.sql file, they can probably do the import, if you're not sure about the operations to do so in PhpMyAdmin.