"I think one way to overcome that would be to require a ⅔ majority - a requirement that should have been part of the original vote given its momentous impact "
In most places a supermajority would be required for a decision of such magnitude and import, even if it were something that could be unilaterally reversed by the country voting.
The people who set up the referendum were idiots. The choices were not sufficiently clear, the impacts had not been analyzed before the votes, there were too few alternatives, and it was explicitly defined as 'advisory only' before the vote and treated as 'mandatory' after the vote.
No wonder things are so f*cked up.