ssh -p 51685 seems to change the port that I'm trying to connect to, not my outgoing port.
As does editing
I want to change my outgoing port from 22 (which is blocked) to 51685.
Are you sure it is the source port that is being filtered? Clients usually use an arbitrary source port (between 1024 and 65535) not the protocol's assigned port, and if your connection passes through any NAT arrangements on the way between you and the server (or the device that is doing the blocking) the original source port will be "lost" anyway so source port based filtering isn't usually very useful anyway.
For instance I've just made a fwe connections using PuTTY and OpenSSH to one of my servers, and wireshark tells me that the source ports for the connections where 6525, 6535, 6560 and 6562.
Outgoing connections do not use fixed port assignments, they choose an available port number, usually higher than 1024. More to the point, unless you are running as root (the admin user account, which is disabled by default on OSX), you cannot open an outgoing connection on port 22 because only root is allowed to open any ports below 1024. Therefore, if you're running
Whatever issue you're having, you have incorrectly identified its cause.