Once I did that, I confirmed it ran ok, connecting to the VPN, running the database copy, and then disconnecting from the VPN. All ran well.
To automate, I utilized a new feature of the Synology Diskstation's DSM software, version 4.2. There's now an integrated Task Scheduler. Interestingly, it doesn't appear to be a simple GUI interface to crontab. Instead it has some proprietary commands and probably data structures. It's also poorly documented. The help file explains what the various parts of the Task Scheduler screen are but doesn't have Synology's usually good tutorials on operating the feature. DSM 4.2 is in beta I believe, so perhaps the documentation will improve when the final product is out.
In any event, it's fairly self-explanatory to set the custom user job up. You give it a name and enter the command exactly as you would enter it at the command line interface, and then set a frequency. You can also run on demand at any time from the GUI.
I don't like that there's no record of tasks in the logs when you run them. Perhaps that will also be improved in the final release. But as it stands, when you run a task it doesn't look like anything is happening and none of the task's output is displayed anywhere.
You have to run this line from the terminal session and it will give you information on the scheduled tasks and what their last run status was:
Aside from the /tmp directory being a weird place to put a main feature, this line will return a list of the scheduled tasks and their configurations, along with a last run time and status.
At this point I have a boat load of error handling and feedback features to add but can now start taking advantage of automation to have this thing run automatically every day.