After a lot of research, I think the only way to really address this problem is to get a separate router and put it between your network and the ATT gateway router. The reason being that ATT’s router is so limited in functionality, it doesn’t offer the tools necessary to accomplish this.
First, as you noted, there’s no NAT loopback. Second, it doesn’t allow you to change the router’s DNS server, which prevents setting up a split brain DNS.
So short of using a new ISP or getting a separate router, I’m not sure this can be accomplished with just ATT’s equipment.