Thanks for the update.
It didn't work at first but I found the problem. The WPFTS Add-on for WP Download Manager wasn't passing the $is_enable_external_links parameter to GetCachedFileContent_ByLocalLink, so it wasn't indexing the WPDMPRO external files.
I changed that, and it did index everything. However, the performance on the WPDMPRO front-end pages was unbelievably slow. It turned out, it was reindexing every file any time it's post was viewed through the front end. So, I set $is_force_reindex to false in the call to GetCachedFileContent_ByLocalLink, and that seemed to fix it.
I don't know whether the changes I made to my copy of the the WPFTS Add-on for WP Download Manager were correct, but there are definitely some changes required there to make this work.
It does appear that this functionality will work as long as WPFTS Add-on for WP Download Manager is updated.