John,
There is no published API for Remote, but it's easy to read the plg_jpremote code as it describes the parameters to all calls.
Technically, what you're trying to do exists! It's the scripts generated by CRON Script Manager. Each of those scripts is actually just a configuration table which then loads croninclude.php. This latter file uses JSON to talk to the JoomlaPack installation and do the backup. Since the JSON service is embedded in the component it doesn't require setting up an XML-RPC plug-in. It's much more compact.
Here's the best deal you've ever had: croninclude.php can initiate a backup on any server, not just the one it's installed in! In fact, I was using this file long before the CRON Scripts Manager feature, on my Linux server, in CRON jobs which would run remote backups and download the archives to my own server. I think this is exactly what you want to do.
If you don't understand the comments in the code, send me a PM with your email and I'll try to explain every step of the process as better as I possibly can.
Nicholas K. Dionysopoulos
Lead Developer and Director
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