From what I'm seeing, it seems that it's not possible to directly access/ manipulate a Network Place from the command line, be it in PowerShell or the plain ol' command prompt.
@slipsec (#13899):
Thanks for the suggestion, but PowerShell doesn't support the port number in the destination path any more than the net use
command does.
So the best thing I can figure to do in my particular situation is bite the bullet and buy something like WebDrive to enable drive mapping via WebDAV on non-standard ports, or do some different configuration (e.g. separate web app with a different IP address and host headers) in SharePoint to expose the site via NTLM on a standard port.