I looked at this, because I modified the plugin to import squarespace images that didn’t have an extension, and noted that the ajax form action posts and receives a list of the articles to retrieve:
{“success”:true,”posts”:[5,353,478,216,354,137,140,355,480,7,356,139]}
Then it continues in the JS on the var data action:
action: ‘external_image_import_all_ajax’,
which goes to the ajax.php file and follows through to the function external_image_import_images.
It does its thing and appears to go through the whole process without issue, but I modified for a specific use (checking pages as well as posts, looking for a specific extension from a squarespace site) and have no idea if it would work for your purposes. Is there anyone that would like a copy to test and see if bulk processing works for them?