Okay, Progress!
I was able to connect to the projector using just an Ethernet cable. It was the most successful connection using that app, Projector Manager by SigmaSix.
I used these specs
Computer -> Static IP
IP Address: 192.168.100.2
Subnet Mask: 255.255.255.0
Projector -> Static IP
IP Address: 192.168.100.10
Subnet Mask: 255.255.255.0
Gateway Address: 192.168.100.002
However, it will not turn back on when I successfully turn it off. I notice that in the Network Settings on my Mac that the Thunderbolt/Ethernet listing will turn Red once the projector shuts down. It will then turn Green when it is powered back up (with a manual button press). Furthermore, I need to manually delete the projector listing and then re-add the EXACT SAME listing to get it connected again.
This leads me to believe that I may need a router in there to ensure the connection is kept and the projector can be turned back on...
I will experiment some more.