when I first entered school in Europe in the mid60's mine was the first generation of pupils that wasnt forced to write with the right hand - as educators had just become aware of problems. So I consider myself lucky, but I couldnt disagree with you (sibelius) more on the instrument question.
I dont consider it a problem when it comes to playing an instrument.
Im a decent fiddle player, (a lot better than most right handed fiddle players I know) my advantage came from an early start, and lots of practice, I dont recall that at any time I wanted to play the other way. (If youre playing folk fiddle, it doesnt matter, butI doubt there are many classical violinists playing left handed)
What would you recommend for a piano student: re-stringing the piano?
Id consider that ignorant and fatuous.

Ive met Ryan Thomson, mentioned above, Ive seen him play two fiddles
at the same time, right and left handed (of course he had a couple of people doing the bowing) an impressive feat.