but that is currently inaccessible and since I want the arduino to use my laptop or desktop's Ethernet plug to connect to the router via wifi, would not work because of the mac address changing in-route.
Then you want to use internet connection sharing. The router can stay exactly like it is. The laptop or desktop ethernet connector will need to be set up for a localnet. That will determine the ip on the ethernet shield. It needs to be a different subnet than the wireless device.
Windows XP would be my choice to try first. Here is how:
The ethernet port on your laptop/desktop computer will be assigned 192.168.0.1. The challenge is the wireless device may also have a 192.168.0.x network address. If that is the case, you will need to change the laptop/desktop ethernet port ip to 192.168.1.1, and use 192.168.1.2 for the ethernet shield.
edit: Hopefully, the Windows XP internet connection sharing program will not assign duplicate ip subnets to the ethernet port. I have not tried it with that setup. None of my wireless APs use 192.168.0.x or 192.168.1.x network addresses for this reason.