ahh, it's not "game hangs ups after space race victory" problem, it's problem like "I wonder how many parts of space ship was built... god dammit game hanged!"
I'd noticed this problem in a CCM 1.8 game a couple of months back, but I'd put that down to it being a Mod (a
very good one, but still not completely de-bugged!).
However, I now seem to be getting it in my current (unmodded) epic game as well.
Although the first Ship-component (Cockpit, I think) was added without a problem, I have suffered several game-hangs ("Civilization 3 is not responding") during subsequent interturns, as additional Ship-components were completed, forcing me to EndTask, restart C3C, and then reload from the last (auto)save.
For me, the hang actually seems to be triggered by clicking on the 'X' on the Spaceship (F10) screen: when I simply press 'Enter' instead, I get taken back to the "What should CityX build next?" pop-up on the main map-screen.
So if you're getting to the Space-race screen directly by pressing 'F10', maybe you could try pressing one of the other F-keys to get out of it?