Really? I agree "a new remote desktop" makes me suspicious about usage over WAN because most all suck. I didn't have great luck with Windows Remote Desktop, either. We went with TurboVNC/VirtualGL on the server and recommended, I think, TurboVNC on the client (via ssh). I used macOS Screen Sharing.app because it wasn't Java and was more comfortable to use IMHO (with things like screen scaling and fullscreen). Most other VNC clients performed significantly worse. I usually ran the desktop around 1440x900.
This seemed to be the best setup with high latency and low bandwidth situations. We had people spanning the furthest time zone.