Anyone use a mediator to close a deal? Instead of opposing counsel?

To share legal costs on a rather modestly sized transaction ($400K), seller has proposed using a mediator, i.e. shared lawyer, to work on getting the deal done. My first reaction was "conflict of interest", particularly when phrased as "same lawyer", but in reality, people use mediators all the time for different scenarios.

Anyone have success with this?

It is a rather small deal, so I'm all for saving transaction costs.