I've thought a lot about this, because my state is heavily gerrymandered, and the legislature keeps voting to undermine several recently passed amendments (abortion rights, marijuana) to our state constitution. They also tried to change the threshold for passing a referendum from 50% + 1 vote to 60%, when it was clear that there was enough support to pass the abortion rights amendment.

You do it via constitutional amendment, which is a popular referendum.

Fuck what the professional politicians think of sortition; do an end run around them, because professional politicians are the problem.

Get this accomplished in enough states, and then you have a level chance of doing an amendment to the US Constitution.