We've had some clients using Backblaze for remote file storage in the past, but I'm not sure if they can still provide the sort of file URL we'd need for Remotely Hosted Downloads to work.
We need a static (unchanging) link URL pointing directly to the file itself (not to a download page for the file) that ends in the actual filename -- e.g. like so:
http://www.example.com/FolderName/SubfolderName/FileName.ext
Feel free to email us with the file URL you're getting from Backblaze; we'll be glad to take a look and see if that would work or advise further if not.
If you have your own Web site, you might even be able to just upload your files to that and provide the URL to each file there; see this help page for tips about determining the URL for your files there, along with further tips here about securing access to files stored on your site.