The problem is not ncurses so much (You CAN capture mouse input to move a 1 character cursor around in ncurses mode on a local virtual terminal), the problem is that SSH is not intended to send mouse data. It emulates an old style terminal, like a VT-2000, over an encrypted data stream to prevent eavesdropping and system compromises. It supersedes the telnet protocol, which was created when the internet was still ARPANET, and when such considerations were not really given, since only authorized personnel was allowed on the terminal anyway-- Definitely before mice were a major fixture in computing.
To get mouse support, you need something like VNC, which then sends full graphics output in a compressed data stream. I would be leery of giving out anonymous VNC access. (and likewise with SSH access.)
You would probably be better served with DFTerm3, which is a DFHack plugin. It claims to be able to permit remote control of a DF session over a special protocol using a remote host connected through a web browser. This limits the connection to the DF process itself (as opposed to SSH which gives terminal access to an account) or VNC (which gives a full remote desktop), and limits what connecting users are able to do. (Though I dont know how secure the protocol is, nor how secure DF itself is. It is possible hackers could exploit DFTerm3 in clever ways, since DFHack is able to modify system memory within the DF process, and thus could be used to do clever stack smashing if you know what you are doing. At the very least, I would suggest enabling execution protection features on the CPU. See your OS's documentation on how to do this.)