Our reader who has tried the pre-ironed coconut from here: http://the-straw-shop.mybigcommerce.com/ asked the vendor if there was a way to make it more transparent. His reply was:

I am so pleased you were happy with your order.
Boiling for long periods of time only breaks straw down, so that's not the
answer..

But, as I leaned from an applique master, you can obtain a more transparent
look by removing more of the pitch of the plant by using a razor blade.
Very gently, begin to shave the pith side of the stalk (the non-shiny side)
away from you and keep removing layers of pith until you reach your desired
transparent look. It takes practice, but once you achieve it, I think
you'll be pleased.

The reader says that it's fairly easy.

Here's a little more feedback from the reader who is using the pre-ironed straw:

I am absolutely convinced that they 'SHAVED' THE STRAW before they chopped it up--you get transparency. And the knife--the act of drawing the blade against the straw--actually seems to burnish the pieces. The resulting product is soft--it's light, fluffy and easy to chop up fine by hand

The back--the unshiny part of the pre processed pre ironed pre dyed straw is called the pith. The front is the shiny part. It doesn't seem to matter which part you scrap with the knife. But it is easier to shave from the pith/back side.

Draw blade in short movements to avoid curls. After just one or two rough chops, the stuff seems to break apart on its own. I got very small light pieces with transparency and shine!
Wish this picture was better--see attached