The Cheap-O-NAS has been running great for the last few weeks, and I've no major complaints. However, it's not quite perfect. A couple of times, I've pulled the power and it hasn't shut down properly and ended up flattening the batteries completely. And on one occasion it didn't boot up properly.
The immediate problem is that the voltage regulation (for the main supply and the battery backup) is quite poor, so the Pi is regularly detecting low-voltage conditions, especially when the disks are thrashed. This can't be healthy, and probably leads to all sorts of odd, unexpected conditions arising.
The solution is to re-architect the supply circuit, putting a dedicated 5V dc-dc supply right next to the Pi, and powering it all from a much higher voltage (e.g. 12V). A suitable switcher has been identified, only requiring a minor modification to bring its nENABLE pin off the board, so that the supply can be shut down. The whole circuit is much simpler than before, only requiring two transistors and five resistors (plus the supply OR-ing diodes).