Why anybody would want a left-handed dulcimer is beyond me.  I've built one recently, though, by special request.

Yes, but most nuts and bridges have a high ridge with the notches filed in it, sio flipping really isn't an option.  Easiest to make a new nut and bridge, and then put new string on the other way around.

Turn them over and make new notches. If it uses a 0 fret just open the slots so he bass string fits will usually work since the nut is for lateral string positioning. Or, you could just play the bass string as the melody [DAd] like a friend did. 

updated by @skip: 02/16/22 04:11:29PM

You guys were so helpful with my last query, I hope you don't mind if I burden you with another question:

I see dulcimers advertised as "right handed" and "left handed".  Could a left handed dulcimer be converted to a right handed dulcimer by simply flipping over the nut and bridge?