Thanks for the response. The router is a DIR-865. I have "Enabled WAN Ping", and in the firewall I have all ports open to the following blocks of addresses, which I know to be owned by SE:

202.67.48.1 -202.67.63.254
124.150.152.1 -124.150.159.254
61.195.48.1 -61.195.55.254
219.117.144.1 -219.117.159.254

Now, if there is some game traffic that is being sourced from some other IP that doesn't belong to SE (like a cloud service or something) then it may be the culprit. I'm not comfortable opening all the ports SE says to open to all IP addresses. I'd rather limit it to just ones owned by SE.