Thanks gstar!
Except for the last checkbox “If no images are downloaded successfully…”, we have the same settings.
Luckily, I tried to import on a new and empty test installation of wordpress and images were successfully added in all adverts. I noticed that newly downloaded images that were not existing in the media library will create a new “attachment” during the import, as seen on WP All Import’s logs. I then remembered that Greg mentioned “attachment” above, which was spot on … thanks Greg!
I confirmed this on my live site by doing a re-import and I unchecked “Search through the media library for existing images…” which will trigger new downloads, and I was finally able to import images successfully.
Thanks again!