How to rice potatoes
What an interesting idea. Essentially you're looking to make rice out of potatoes, yes? 

I can see a couple of options. You could make potato orzo (a small pasta that looks like rice) I suppose; googling recipes for potato pasta should point you in the right direction.

You could also, I think use the reverse spherification method. Make mash as you normally would, and then put it through a ricer into an alginate bath. This should preserve the individual 'grains'. You will need to have milk and/or cream in the mash to ensure there is enough calcium for the alginate to react with.