Can you turn off shadows and see if it still happens?
I have shadows on high instead of ultra, and I've been doing some (not-so-comprehensive) testing with different graphics settings. It may, in fact, be a GPU issue rather than a CPU issue, and I hadn't even considered that, since the entire engine seems to freeze save for music.
The default Anti-Aliasing in Knossos.NET is actually SMAA Low, and I decided to try FXAA instead. With only an 8 minute mission, I encountered no freezes with FXAA and Shadows High, which I realize is anything but thorough... Still, I'm going to see how it goes next week.