Getting Windows to use a high resolution for VNC headless

I have a Win 7 Pro x64 machine, which I run without a monitor and coect to via Real VNC. When I coect a high res (2560x1600) monitor to it, then I can select that resolution, and VNC lets me use it as well. However, the second I discoect the monitor, VNC downgrades the resolution to 1920x1080, even though VNC shouldn't care.

How can I keep the VNC resolution high?

I've tried using the NVIDIA Control Panel, but it won't let me add a mode.