Stop using HTTP for everything. Invent your own protocols. Be cool, be creative!
In fact, don't even use TCP or UDP. Run your new cool protocol on top of ICMP, for one. Or invent a new cool transport-layer protocol. Shit's broke? Tough luck!
@cjd fun fact. I threw in a quick translation layer that masquerades UDP as TCP. And it works, even across NAT! I need to finish it properly and publish the code some time.