OK, flash of inspiration for the Venture Star's engines came while rollerblading door to door at work, specifically how to cool them.
Use regenreative cooling!
Now, this may seem like a bogus concept when dealing with antimatter, but bear with me. this may take a bit to go through.
1. Antiprotons and protons are contained in a magnetic bottle in the engines. However, the mixture of matter to antimatter is very matter-rich, ensuring complete usage of antiprotons.
2. The violent reaction of the matter-antimatter collisions results in a flood of energy entering the reaction chamber, massively raising the temperature, and generating plasma. this is then directed out the back of the nozzle as the working fluid.
3. Additional liquid hydrogen is continually flowing around the chamber to provide cooling. Hydrogen is an excellent coolant, because of its high heat capacity. This is also raised to extreme temperatures, and is ejected into the exhaust stream to add thrust.
This ensures that you only need the radiators during the coasting after shutdown, as we see the Venture Star on arrival at the start of the movie.
The radiators are still wrong, though. No argument from me.