A few years ago I came with a decent solution for this problem:

first, the backup machine is set up to either accept etherwake packets or a run crontab job both at boot and daily (while the machine is powered up, of course) which runs rtcwake to set up a wake-up timer at the machine's RTC clock;

then, you can either wake up the backup machine with etherwake or wait for the rtc timer to wake it up, copy data over to it using rsync or something similar, and suspend it to sleep.

As far as I know, ACPI sleep uses about as much energy as leaving the machine plugged but turned off; The only extra stuff running is the refresh circuits for the memory, which is powered by the stand-by power supply and uses very little energy. The only drawback of such a system would be if a power outage happens, the backup machine needs to be manually powered up and then suspended. This can be made easier by remapping the power button to suspend the machine instead of powering it off, so someone at the mill would only have to press the power button, wait a couple minutes until it's fully booted, and then press the button again so it suspends. A more ideal workaround would be having some kind of battery powering the backup machine, and maybe telling the machine to go to sleep in case it detects it's running on battery.