How would take care of the edges of the doorways ?
You could frame it with finished ends to make the pieces like trim around the doorways.
I would recommend trimming with 1x4 boards and do not miter the corners. That will keep more with the true shiplap motif. Our farmhouse was built in the 1880's with shiplap everywhere and that is how it is finished.
Exactly what Shore grandmom suggests. Use the same boards for the shiplap and use them like trim around the door.