I realize this is a 3-month old post, but I sat with this problem as well (I too have a 6990) and it took me a good long while before I figured it out (solution 1 didn't exist yet).
There are two solutions:
1. Download the newest version of Catalyst Control Center.
Open CCC then under Gaming->3D application settings scroll to the bottom where you will find AMD CrossfireX mode for 3D applications, set it to disabled. Scroll back up to Application profiles, select save and find the executables for Haegemonia. All done.
I'm getting a bit of flickering in the top right corner with this one and the window border shows from time to time. Could be i just have to play around a bit with the compatibility options.
2. Download DXWnd here:
http://appaholic.co.uk/wp-content/uploads/2008/03/dxwnd.7z DXWnd will force the game into windowed mode (and windowed mode will only use one core). Just unpack it anywhere you like and open dxwnd.exe as admin. Under Edit choose add, click the browse button find the executables and I have through trial and error found the best options to be: tick the box "DirectInput is Hooked" and under Initial Coordinates and Moveable Range in the 5th and 6th box type in your resolution. Press OK and right click the *install path*\hgm.exe (or hgma.exe for Solon Heritage) in DXWnd and choose execute.
This option gives the best image quality (no flickering etc.), but if you launch Haegemonia from somewhere not DXWnd it will still be launched as windowed (IF DXWnd is currently running with admin rights).If that's the case, you won't (in my experience) be able to control the camera with the mouse, it will point downwards and keep spinning until you release the mouse button.