Well, so I haven't resolved my prior issue with the Airport Extreme Base Station, but apparently it's a widespread problem with the latest firmware update 7.2.1. Apparently that latest update caused a ton of other problems too (connection problems, NAT problems, and AirDisk problems).
Anyway, one thing came to mind as I was playing with my AirDisk - there are routers out there that act as HDD to store downloads directly without going to the computer and back out again. Is there a way to set up the AirDisk so that my downloads move into it automatically?