The 'best of' approach is ok for deciding who wins a game of conkers or tossing a coin for whose round is it next but has no relevance for how a country takes it's most important decision for decades.
Besides, with that statement you are already assuming that another vote would result in 'remain' coming out as the preferred position. If, as most leavers insist, it still is 'the will of the people' then a second vote should result in a much needed affirmation of the first. As 'the people' would have voted with the awareness and information on the reality of leaving that we now have, if we as a country still vote leave then pretty much all arguments to the contrary are null and void and we just get on with it, nuff said!
If however a second vote results in 'remain' decision, once again all those fiercely defending 'the will of the people' get a result as 'the people' get a chance to change their mind over the biggest single decision for this country for over fifty years. We could then decide how we want to proceed, another vote (best of 3 like in the kiddies games), simply remain or something else.
Now we are faced with the inevitable delay anyway why not use it for a double check, what's to lose?