It's been done successfully many times in many countries. Look at Britain for example. Say what you will of the problems they have now, but they're undoubtedly better off than when they were under the thumb of the monarchy and the aristocracy. Gradual changes in the law punctuated by occasional serious strides forward led to a near complete abandonment of the previous system.

I'm very skeptical that any group capable of a violent revolution would be effective leaders. The founders were a rare group of brilliant men. The Constitution can be amended, that should be enough.