Changes made are saved in a device mapped off /dev/nvram, which I assume is "Non-volatile RAM". All changes you make on this router are persistent even after a power cycle.
But yes, I don't want to waste anyone's time. I'm not comfortable messing around with this router like that, especially given the references to br0 in so many places.
If there's no way to fix it from the Arduino side I'll "borrow" a router from work and if that fixes it stick with that.
Seriously though - this thread has been very valuable to me, and I greatly appreciate everyone's help.