IT WORKS!!!
*facepalm*. So it's definitely my LAN MAC address that needs to be used. However, when I had tried the LAN address before, it didn't work because I needed to REBOOT MY PHONE!!! It finally occurred to me when I thought, "Hey, whenever I make firewall iptables rules changes in Tomato or DD-WRT, I always have to reboot the router to make the changes take effect."
So, I put in the LAN MAC address, rebooted the phone, and voila! Can't connect to the internet!!!
Now... I guess I'll have to use the "arp -n" code in a terminal app in my friend's son's phone while connected to the neighbour's router. I was just planning on using the BSSID of the neighbour's router... but clearly that won't work.