It works great! Many, many thanks. (I bumped your karma

I had it working (i.e., I was getting the "Database backup created and sent!" message on my screen when I ran it manually) but the email was not arriving. I had been under the impression that the code didn't need any personalization because it picked up everything necessary from my cmsms config.
I found that if I replaced "youremail@example.com" with my email address in the top lines of the code, it worked fine. (My config.php doesn't have my email address.)
Also, when I set the cron job using cPanel, it asks for my email address. So between the two email specifications it is now working fine as a cron job.
Nota Bene: For anyone setting up a cron job, be sure to append "> /dev/null" to the example given above, so it looks like this:
php /home/your_name/public_html/backups/backup-database-cron.php > /dev/null
(as mentioned above by chilsta)
It's also worth noting that in setting the time for the cron job, the time specified will be local time for the location of the server, not necessarily of the user.
Thanks, again, Elijah.