Okay, I think I found a solution.
In the Dokuwiki configuration manager, in the Advanced Settings section, is a "sepchar" setting. This setting unfortunately only allows the admin to select "-", "_" or "," as the sepchar, where I would like to select a space instead. So, I went to my local.php file (in conf) and included the line:
$conf['sepchar'] = ' ';
Dokuwiki seems to be fine with this. No errors so far. However, any previously created files in your Dokuwiki install will now be useless. (dokuwiki won't pick them up any more, bleh.) To the rescue comes Linux and being able to rename files with regex. Using a space for the sepchar causes DokuWiki to replace the underscore with a + in the filenames.
So, this_file.txt now becomes this+file.txt. To do the renaming I used the Linux rename command like so:
rename "s/_/+/g" *
:)