What did finally work for me though was I noticed in the DNS info on the Apple TV that it was seeing both the default gateway IP (the router) and the DNS server I have my router set to (1.1.1.1). So, I changed the DNS setting to manual and forced it to look to the default gateway IP address only. Soon as I did that the Prime app suddenly came back to life, even with the rest of my network setting set to automatic DHCP.