Just upgrade from OE to LE 7.0.2-2 for my MX-III 2GB and finally it's possible to save the IP assigned over reboot...
I have a MXIII 2GB box as well, which exact version of the LE firmware did you use? MXIII-1G, S82, M8 or T8?
Your answer will save me a lot of trial and error! 
Is there maybe a script I can run, to change / spoof the MAC address of one of the boxes?
I also begin to wonder if the problem is confined to v3_1 boards. Can anyone confirm that they have purchased multiple boxes of the same motherboard version and have different MAC addresses assigned to each, with these builds?
Hi, try this. It solved a similar problem in OpenElec on a S812 box, using the info from this post on Freaktab
the MAC address has been rock stable since but you have to pick one yourself.
You can change the MAC address with a udev rule.
SUBSYSTEM=="net", KERNEL=="eth0", RUN+="/sbin/ip link set dev %k address 00:00:DD:6A:6B:C7"
(change the address to your needs)