Wanted to share an update on this, for people like me who found lots of people with the same problem but no solution in sight. I ran some ethernet cable through my wall, so I’m on a wired connection now, and I haven’t had this issue since making the switch.
I’m not sure why the wireless connection was an issue for WoW and only WoW, but there you have it. Not a satisfying answer, I realize, but it’s at least confirmation that the “try using a wired connection if possible” advice does have some merit, even if it isn’t always practicable. Luckily in my case it was.
I will reply to this topic again if the issue comes back.