Can't connect to PS4 Remote Play. Is it because of the firewall, and is there a way to get around it?

I went through a good deal of work to run cable and plug my PS4 into ethernet, just so I'd have a better time using the Remote Play feature when I'm out of my house. I planned to use it at work (we have a good bit of downtime on occasion), but, come to try and use it, the application can't connect to the PS4.

The error code I get varies-- I just tried it again and got 0x88010c36. But I have successfully used this elsewhere: in other rooms at my place, my girlfriend's, and at a coffee shop. This kind of leads me to believe that the firewall at my work is preventing the Remote Play application from getting through.

Does this sound accurate to anybody else? The only reason it seemed kind of odd to me is that I'm able to get onto Steam and download/play games just fine. Does anybody have any suggestions for getting around this without telling my work "please open a port in your firewall so I can play my PS4 here?"