You could try using ShippingCart[1] by LBC. I actually use this site frequently if I purchase items from Amazon to be shipped to the PH, simply because the shipping fee is cheaper and it's a lot faster. Tried ordering from Amazon straight to the PH in the past, and it took more than 2-3 months that I actually forgot that I ordered something from Amazon.
Depending on your package size/weight, just make sure to check how much fees you're going to pay. They have a shipping estimate tool on their site.
P.S. No customs fees as the package gets delivered straight to your door.
[1]
https://www.shippingcart.com/