Solid work! It stays close to the original, but takes its own liberties. As soon as the voices came in at around 0:15, you won me over.
My two gripes were: 1) The flutes are a bit too solid. I feel like they should be "stuttering" more, instead of being continuous notes. You can check the original for reference, but yeah, I really think that's something that should be kept. This is my biggest concern.
2) The voices get a little chaotic at around 1:15. This is more of a stylistic choice and not something I can fault you on; you just tried it out and I personally didn't like it. I'm sure others would be perfectly fine with it. I just thought the voices were changing pitch a bit too quickly, kinda detracting from the ethereal feel that you built at the beginning from 0:15 onward.
That aside, excellent job! I love hearing Forest and Shadow Temple remixes; they just give such an awesome, otherworldly feeling that I think is lacking in newer games. Keep it up!