Hey Peter,
Thanks for reaching out.
I’m sorry to hear about this issues—I’m also a bit stumped about them, because I cannot recreate any problems with the Media library in any view. We also don’t have any other reports of this sort of problem, so there may be something happening on your site that is unique to your site.
For reference, here’s a screencast I made of my own local testing site. I’m using the latest versions of The Events Calendar and its premium add-ons, as shown in the video, have no issues with the Media library whether in Grid View or otherwise. ? https://cloudup.com/cpn-8JaeXuV
You mention having done extensive testing with plugins — what about with your theme? Do you find anything different if you deactivate your currently-active theme and activate a default theme like Twenty Twelve, Twenty Sixteen, etc. instead?
Let me know what you find.
Thanks!
George