Mac mini's DVI transmitter is pretty much on the edge with 1920x1080 already, there are even some extra bits in the driver to workaround some issues even in that resolution.
Resolutions like 3840x1200 are pretty much out of the scope for most of our supported hardware. The typical max is something like 2560x1440/1600 for some Radeon cards which have dual DVI support, typically found in the PMacG5 range of supported machines or external PBook output.
Unless we expand our support for PCIe graphics cards, I don't see how this monitor can ever work properly in its native resolution.