Sorry I can't be more helpful, I can only point in the direction of possibilities, not having had to calculate Geodesics myself.
One option I just found via NuGet
Another option might be one of the ports of JTS to C#. One of these is (can't remember, there is another one as well...http://code.google.com/p/nettopologysuite/
Another .NET spatial library is
Yet another option may be http://sqlspatialtools.codeplex.com/ in combination with Microsoft.SqlServer.Spatial.Types assembly. There is a Nuget package of the same name and it comes built in with Sql Server Express (or standard) from version 2008 onwards. Don't be fooled by the Sql Server name though, you might have to use Sql Server types, but you can do spatial operations entirely within code. Pretty limited though, especially projection wise.
All of the above have NuGet packages, so load em up, and try em out.
Unfortunately, none of these is really obvious how to get the geometry of a geodesic, but with some projection love, I reckon it would be doable.
My thinking, although it may well be wrong, would be (using perhaps the System.Spatial) to create the line as a Geography type, then reproject to your target geometry type SRID. My knowledge of Geodesics is foggy at best though.