I love this idea that more democracy is somehow less democracy.
It's like saying we should have one General Election and then never have another, because doing it again would go against the will of the people.
The fact is the situation has changed and the initial referendum wasn't clear enough. Leave didn't mean Leave - it meant leaving in a certain way.
So the answer, to me, is obvious - go back to the people and ask them how they want to leave, and at the same time give them the choice of changing their mind altogether.
This is why referendums tend to be non-binary, because they're obviously subject to interpretation. Having the result of that referendum as binding would have been lunacy.