And if a re-run ended up with a small margin in favour of staying in the EU then would that be a good basis for remaining?

We've got be grown up and just accept the outcome, whatever the margin.  There isn't an alternative, as you can't stay in if the majority votes out, and there isn't a way of being partially in.

I don't see the point in dwelling on the outcome.  The decision has been made, so we all need to work together to make the best of it