A number of dynamic DNS services such as noip.com offer a port redirect feature for just such blocks - when setup your game can connect to the new hostname at port 80 which will in turn connect to any Host/Port that you desire.

If you've ever owned a DLink device you can get a free account with dlinkddns.com by using the serial number of your DLink device as part of the signup - not sure if they offer a port redirect but considering a dynamic DNS account with no expiration requires a subscription and considering the vast number of dlink devices out there with users that never make use of the dynamic dns service offered?

Buying a cheap Dlink router off ebay and using its serial number can be considered as a cheap one off payment for a quality DDNS service - all the better if you get a cheap router that's compatible with dd-wrt which when setup gives you a super powerful device (I use mine as a range extender)