> What we don’t want is direct democracy proposing amendments.

I think the opposite. That is exactly what we need. A lot of the problem we have come from the fact that the constitution speaks almost entirely in terms of what various government bodies do and provides no way for the people to directly override government actions they disagree with. This has led us to our current situation which is based on politicians exploiting loopholes (e.g., gerrymandering, stacking various judicial/administrative posts, manipulating voting laws, etc.) in order to preserve their position against potential electoral response.

In some cases these problems have been overcome or mitigated at the state level. . . via ballot measures. In California, for instance.

> California is a modern example of why republics are more stable than pure democracies, for anyone who forgot about Athens.

I'm not sure what you mean by this, but from where I'm standing California looks a lot more sane and stable than the US as a whole.