First, we are talking about the young Thai coconuts, right? These are the ones that have been shaved so they appear white with the conical top. Those are the ones for the primo water.
With those, the meat is really soft and just scoops right out with an ice cream scoop or spoon.
You can make fresh coconut milk (but you'd need to reserve the water of one of the coconuts for this). I also make a raw porridge with the meat, with a bit of banana, walnuts, and cinnamon. There used to be this AMAZING young coconut meat dessert I would get at the farmers' market in Berkeley, but I haven't been able to replicate it or find a recipe. It was this fluffy concoction similar to a tropical delight (you know those?), no sugar, very Paleo before I knew of such a thing.
"Let food be thy medicine and medicine be thy food." -- Hippocrates