How do I finely strain fresh coconut milk? I had a lovely bunch of young coconuts. I extracted the water of most of them, and I blended all the meats and enough of the water (in the right proportion) to make something like 3 gallons of coconut milk.

The only issue is that the milk has tiny coconut particles that I need to be rid of. I tried a fine cheesecloth (with multiple layers), but draining it is going to take days and if I force it, the tiny particles slip through. I thought about using a kitchen centrifuge, but I don't have one (if they make them).

Any ideas to extract a completely smooth solution from what I've got? The 100mL of said nectar I got from the cheesecloth after much patience, has tantalized me.
Alton Brown made coconut milk on his show Good Eats a few years ago, and he suggested using a clean tea towel and squeezing the pulp until it has given up all the liquid.

Here is more on it: http://www.foodnetwork.com/recipes/alton-brown/coconut-milk-and-cream-recipe/index.html