Thanks to all for the help.  I think all of the ideas were good except 
that they don't happen to work with ISO files and almost everything I have 
is in ISO files!

Here's some more info on what I've tried:

It looks like VLC for iOS will be supporting smb protocol soon:

https://forum.videolan.org/viewtopic.php?f=36&t=128455&p=431357&hilit=ios+smb#p431357

Meanwhile, I thought I might be able to buy an app that would make this 
work.  So far, it hasn't worked.  I installed this on the iPad:

https://itunes.apple.com/us/app/filebrowser-access-files-on/id364738545?mt=8

Now I can see the ISO files on the Linux servers SAMBA share, but the next 
problem is that the .iso file type isn't associated with VLC, so I can't 
click on it to load it into VLC as if it were a local file.  The 
FileBrowser does offer the option to stream the file to a program.  If I 
do that, and stream to VLC, it will open an http connection -- I guess the 
FileBrowswer becomes a web server -- but that doesn't work.  VLC can't do 
streaming of ISO files by http, apparently -- I tried that already using 
Apache on the server.

So nothing is working and maybe nothing can work until VLC supports smb, 
which is supposed to happen within a month from now.  We'll see about 
that!

Mike