John, I came up with a different method to get the flesh out of split coconut halves, in 4-6 lg pieces ... I just slip the tip of a hardened steel new-haven style (curved tip) oyster knife between the hard shell and the flesh, and lever the flesh away from shell with lateral pressure. It usually pops out several large chunks. You can help it along with a few slashes of a box cutter (a single big X, from side to side, is usually plenty). Once the flesh is out, you can optionally peel off the bitter, but I usually ignore it, because removing the bitter takes more work than getting the flesh out of the shell. Anyway, I just sit my food processor with a fine shredder wheel, and feed the large pieces whole though the feed tube to shred it. A grater wheel can sometimes work well, depending on the patter, but they tend to gum up with fresh coconut, and work better with dried coconut kernels. Once finely shredded, just follow the usual method to make coconut milk, by grinding it with warm water in a sturdy blender, and then straining and squeezing in a buttercloth bag. The first milk will be rich, then you can reblend the pulp again with more warm water for a weaker second milk - which I usually combine with the first. Cheers.

The blade should be longer and the grater should be at 90 degrees. This allows the coconut to be held on the chopping board.