So over the past month, I've been providing dumps, network traffic logs and network diagrams to ASUS. And yes, they did just fix the problem in 3.0.0.4.386.44266.
> Modified the DNS setting and router's DNS can be assigned to the LAN side DNS.
At the beginning, I didn't think WAN DNS played a part, but when I repeated my steps a third time, that narrowed it down. I could either have Internet, or use my local DNS. Not both.
I'm very happy with the fix, though I had to spend a significant amount of time with filling out lots of paperwork.
Sorry for the lack of updates. I just felt my time was better spent working with the support staff at Asus since it took a lot of my time.