Why not have your program just listen on port 80 on an address under 127.0.0.0/8?

You will need to run

  sysctl net.ipv4.ip_unprivileged_port_start=80

before you start, but after that you have 2 ** 24 addresses to choose from. And the browser will be happy to treat it as a secure page as well as do proper cookie isolation.