Changing Mac address of the router is a little paranoid. For GGG to get that information they would need to do an ARP request or similar from the PC running PoE.
It is possible that GGG are reading the Mac address of the PC and sending to their servers via an in game channel... I think this is unlikely because it would violate privacy laws in New Zealand as the game would be acting like spyware.
But changing your internet facing, routable, IP address is the simplest, if possible, way to avoid the IP ban. The other way is to utilize a virtual private netw0rk (basically, using another ISP)
I have been banned a great number of times in PoE, in the early days of EB, and I get back up and running quickly as I use virtual machine 'golden image' that I spin up new machine instances of and configure each with a separate virtual private netw0rk. From GGG's point of view these are separate computers running from different parts of the world.
WIMM