Exceptional plugin

Worked perfectly!
Step 1: Ask your hosting company to move all the media files from wp content -> uploads of the old site over to the new site
Step 2: Use the Bulk Media Register on the old site to export a json file
Step 3: Use the Bulk Media Register on the new site to import a json file
DONE! All the images appear in the new media library with their correct date, alt text and title.