edit: btw, keep us updated. I'm curious what the conclusions are.
Resolved January 3rd with no help from Ubisoft.
I began investigating a different issue that was apparently related. I got a couple reports that Garry's Mod (and probably other Source-engine games) could not reach particular servers. In this case, the game doesn't try to hide details about the server or port number it's failing to connect with. At first, the reports were all different machines with NFO Servers, but I later found that all external hosts were unreachable. Knowing the hostnames and port numbers, I set up connectivity tests to verify that an upstream provider was blocking port 27015 (and possibly other related ports too).
With standard port 27015...
External-to-external: Connects fine
Internal-to-internal: Connects fine
Internal-to-external: Fails
External-to-internal: Fails
With alternate port I chose at random...
External-to-external: Connects fine
Internal-to-internal: Connects fine
Internal-to-external: Connects fine
External-to-internal: Connects fine
We identified the upstream provider that was doing this and notified the operator. With proof, they finally realized their system was doing this after they initially denied blocking any ports.
They fixed it that morning. During lunch, I tested The Division and found it was also working.
Speculating: Probably a junior tech at the upstream network implemented the block to mitigate a DoS attack and left it configured that way indefinitely.