The best way to configure UVerse is to use the "IP Passthrough" feature on the Firewall tab of the router provided by AT&T. Doing so allows you to declare a single one of the LAN ports that will have all traffic simply passed through (similar to bridged mode). You will need to know the MAC (hardware) address of your AEBS's WAN port to set up IP Passthrough. Doing the above essentially gives you two networks to work with in your house. One is what I consider a "semi-trusted" network using the LAN ports that are on the AT&T router, and then a fully trusted internal LAN using the AEBS as a router and WiFi AP.
You can and should disable the WiFi radio on the AT&T router but need to leave their DNS and other settings alone if you want your UVerse TV to work correctly. By using the UVerse IP Passthrough port to your AEBS's WAN port, you get the benefit of eliminating double NAT, while now having full control of your internal LAN. I personally don't trust ANY ISP with any part of my internal LAN or WiFi.
You also can still make use of the remaining Ethernet ports on the AT&T router for things like your UVerse TVs, Roku, game consoles, etc that simply should not be on the same internal network as your Macs, PCs, printers, NAS, and mobile devices. If you really wanted to, you could also leave the AT&T WiFi radio turned on for a guest network but I'd rather control that from the AEBS as well.
I would lastly suggest changing the DHCP settings on your AEBS to use 10.0.x.x private addressing (less likely to conflict with the AT&T router's internal addressing), using OpenDNS for DNS, and IPv6 Link Local settings on your AEBS.