WP_Widget dynamic field array with external AJAX

I’m not sure I fully understand what you’re trying to achieve, but I’d suggested to attempt to construct the field’s ID and name from data you’ve got available from the source code of the generated widget. If you check out the code, you’ll find that by every widget, there’s a hidden form field called id_base and widget-id – this should be enough to figure out the correct field name, right?

Developer tools screenshot of text widget's source code