After trying a few approaches, such as soaking in vinegar overnight, and looking online, but nothing working, my wife went to a chinese search engine, and quickly found out that rubbing salt into the holes makes it actually pretty simple to clear out the holes. Not sure about the actual chemistry of how this works, but it looks like a combination of small salt particles being pushed through the holes and actually reacting with the protein.
So far, I've only used this with a wet sponge, fine sea salt, and rubbing from the inside out.
update: While salt works, rubbing it in is still a bit cumbersome. I now use a small metal-wire brush instead, which works much faster.