Moving or Copying Files: Painfully Slow, Loss of Data

If you're using "Open in Explorer" I think that may be part of the issue, and I'm assuming that you're using Internet Explorer. From personal experience I never really got on with the piece of functionality. It worked well back in 2007 when I first used it, but now there are much better options available.

Option 1 - Move To

When you visit a document library in the modern experience, you can click on the ellipsis against the document and select move to (see attachment "Modern-MoveTo.docx". In Figure 1, you can see the option to move to, and then in Figure 2 you can see that you have a number of options to either move it to OneDrive for Business or to another SharePoint site. When I tested this with a document of approx 1mb it took about 5 seconds to get itself warmed up and then do the move.

Option 2 - OneDrive Sync

The alternative option which has been mentioned before is to use sync (see attachment Modern-Sync.docx). In Figure 1, you can see the ability to Sync your library to your local file system using the OneDrive Sync Client.  By hitting the sync button, you'll see it connect to your sync client (Figure 2), and then it will be available from your Windows Explorer windows (Figure 3). Once it's been synced, you can copy and paste documents between synced libraries in the same way as you would with normal files. Again this took only a few seconds to copy, paste and sync between the libraries.

I hope this approaches are useful and that they work. If not, please let us know and we'll see what else we can come up with.