I discovered that there are some big quena Andean flutes tuned to low D which have a mouthpiece very similar to an Irish low D whistle: that mouthpiece is called “pinquillo” mouthpiece because it is the same as a small Andean flute called pinquillo. Please see this link:
http://www.boliviamall.com/catalog/product_info.php?cPath=428&products_id=11984
I wonder if anyone had the chance to play such instrument ? They cost very little: around $ 30.00 if made with cane, or around $ 45.00 if made with hardwood.