Short of hacking core code, the only other way involves a symlink from repository for 'moodlebackups' to point to the true location of the directory containing the humanly recognizable backup file names.
In your shared environment, that's another thing that may not be allowed or, if allowed, provider would have to do that ... protections for customers on the same physical server. Just one caution, if you use cPanel find out if cPanel follows apache (cPanel) symlinks. If it does, never remove the symlink from repository using cPanel or anything apache related cause the contents of the directory will also be removed.
Another thought as well (there is alway yin/yan and catch 22's! :\) ... full site backups will include that directory (which is good), but full site backups will be larger than before. If you have a shared package that limits space usage, that could bite ya IF changing config to 'backup area' AND 'designated' ... which is an option! You'll have one backup in the moodlebackups and one backup in filedir.
If someone else knows another way, please share! ;)
'spirit of sharing', Ken