cURL ports not open - any viable alternative?

I have a client hosted with GoDaddy - but they're quite restrictive with their service and don't allow very many ports to be open.

I have a script that needs to communicate on an arbitrary port (1129) via cURL but of course GoDaddy won't have any of it. Is there any alternative that I can implement to still confer with the target source on port 1129 but bypass the need (at least on the server's end) to use port 1129?

You could use an SSH tunnel.

I guess you could use sockets but on the other hand GoDaddy may not allow that also. Changing the hosting company might be the only solution.