Hey Don,
I know you're looking for real quick solution. I just took another look at the specifications and CNET review for our routers and they are virtually the same.
The first ATV 3 I tried to set up a year ago was a very frustrating experience. Once I set it up with the ASUS router, it came to life.
With the ATV 3 I bought last week, I expected issues so I read the enclosed instructions a few times and learned that by ReSetting it via a Micro USB cord, make sure it will handle Data, the first one I used did not, and connecting it to my Mac and used iTunes to ReSet the ATV 3, it instantly and flawlessly found my WiFi LAN and allowed me to proceed with connecting it. (While in the iTunes connection, there was very little in the way of progress notation and I did experience a few Time Outs before it finally took the ReSet.)
I revisited my Router Console Page today also to refresh my memory about the various settings I have enabled or not. I did discover I had not UpDated the Firmware which I did do today.
Usually, it is the simple and little things that hang us up when we're in a hurry or not quite seeing the obvious in our rush.
I would encourage you to try the Micro USB/iTunes ReSet for the ATV 3 and then see if it doesn't respond as it should. This will take it back to Factory Reset and then install the current OS Version. Probably why it took so long, even when connected to the Mac at 5GHz and only 8 feet from the router. In this location, I've been getting 110 to 140 Mbps so I believe the ATV 3 is slow to receive, digest, and install the actual OS updates. And the USB connection is probably USB 2. Stuff takes time to get through to the end.
I was going nuts with this last year and just knew it had to be easier than it was for me. I certainly feel your frustration and hope you can work through it.