I emailed support after several hours and got a response from them, so I thought I'd post it here just in case anyone else has this issue:
"We close no ports, so you are welcome to request this via a script if you
like. Active listening on any ports are not able to run on our shared
servers though, if this helps a bit. Feel free to let us know if you have
any other questions though, and we will reply as soon as possible!