Blocking Clash of Clans

My kids play Clash of Clans (CoC) a lot and I'm a bit worried about the addictive affect it has on them.  I want to limit access to CoC on my home network so I started researching how it could be done.

I have a Netgear WNDR3700v4 router that sits between the home network and the internet.  I also use OpenDNS to filter DNS searches.

The simplest way to block CoC with my setup is to block the port that CoC uses -- 9339.  On the Netgear router, click on the Advanced tab.  Then, Security, Block Services.

Click the Add button.  Then, fill out the fields as follows:

Service Type: User Defined
Protocol: TCP
Starting Port: 9339
Ending Port: 9339
Service Type/User Defined: Clash of Clans
Filter Services For: All IP Addresses

I could have only filtered the IP Addresses of my kids devices but that may change and it would be easy for them to get around.

Some web sites say that you can block access to Amazon's AWS servers since Clash of Clans is hosted on AWS.  However, I tried blocking keywords aws.amazon.com, amazonaws.com, amazon.aws.com.  Nothing worked.  I could still play CoC.  I searched the internet for the correct URL to block but I can't find it.

My Netgear router has a log that supposedly tracks every website that the devices go to, but it does not record CoC activity.

Finally, the Netgear router is very limited with security.  You can setup a schedule for blocking ports or sites but you can only have one schedule.  Plus when you block stuff, the scheduling settings apply to all of the things you want to block.  I'd like to be able to block some ports Always, and some ports on the schedule.  You can't do that.

Most home routers are limited like this.  Even the dd-wrt software has limited features.  I guess I will have to buy a commercial router to do what I want.