Once you have your core game all patched up, all you have to do to is hold down "a" and select a base part. This will remove the base part's double as well as all those from the detail parts attached to it.
Warning: This will make all new parts attached to it asymmetric.
When you start hitting it high on the complexity meter, just do that and you should get it down a few notches, ready to add more to your vehicle or spaceship.
If you still need to add a symmetric part, you can still use a flat, square block and move that into the already asymmetric base part, but don't forget to hold down "a" first to get even more out of Miss Complexity.