That "add row" will always behave that way if "allow creation of records..." is enabled for the portal's table in it's relationship over in Manage | Database | Relationships. You'll need to either specify validation rules that require data in every field or remove this layout option and use a set of separate (probably global) fields and a script for adding new portal records. You could, for example, put a set of global fields in a popover. The user clicks the popover to open it, fills in the fields and clicks a button to add the data in the fields to a portal record created by the button's script. The script can check to make sure all fields have valid data before adding the new record and can clear the fields after the new record has been created.
Ok. Thank you for all the options! :)