[Christ]

Try ducting your fresh air intake either below the car, or to an area that doesn't always get sunlight or air flowing over hot parts. Somewhere under the car usually stays slightly cooler due to the lack of sun, and the airflow there is generally somewhat cooler as well.

It won't get "cold", but it might help a little. Other than that, consider personal comfort rather than making the car a colder place to be. A small ice chamber with fishtank lines through the seat back and bottom with a small pump will function far better than running ice water through the A/C condenser, and take less space/weight for a 10 minute trip. Turn the pump on a minute or so before you leave on your trip, and the seat should cool right down for you.