Some time later...
I finally opted for the solution outlined in my previous post: "mount everything from the SD card, configure a script to rsync /storage to a remote server daily, and deal with corruption when it happens". Since then, the device has been switched on and off almost daily, no one has ever bothered to shut it down properly, and it is still running.
My conclusion is that card corruption is an issue that must be taken into account, but not exaggerated; a good backup strategy is probably "good enough" in most cases. Thanks for your help.