How do I finely strain fresh coconut milk?

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.