Terry wrote:
..My question is will the dishes dry faster if I leave them inside with
the door closed (while warm) or open the door and let the water
evaporate?

The heat accelerates the drying process, but the steam may inhibit it.
So the most efficient solution may be to open the door immediately after
the wash cycle completes to allow the steam to escape, then close it to
to have the heat help dry the dishes.

As others have stated, conduct some experiments and post the results.