I have solved the problem--at least for me.
Again: I have Windows 10, Firefox 63.01.
Firefox no longer supports Adobe Flash out of the box. In fact, Mozilla (maker of Firefox) plans to completely end support of Adobe Flash by 2020.
So to get the
Manage Attachments [Advanced version] window to work properly, I had to download and install Adobe Flash. After doing that, and after restarting Firefox, the
Manage Attachments [Advanced version] window had a black rectangle where the "Select files to upload" button should be; I clicked the black rectangle, and a popup asked me if I wanted to allow Adobe Flash for this website. I answered "yes", and now I can use the feature.
You can download/install Adobe Flash here:
https://get.adobe.com/flashplayer/
-boster