After a painful amount of time I was finally able to figure out what URL’s are used for Blizzard games via an extensive packet capture. Here’s my list:
Bliz content providers:
This one may be from a different game, but it’s clearly the same CDN:
Here were the two got’chas for voice:
Without those last two I was able to play every Blizzard game (with the exception of Overwatch as it requires voice) I tried, but was unable to authenticate their voice servers.