What procedures should I go through to successfully immigrate to Diaoyu Island?

That's a good idea. First, you must apply to the government of China. It is estimated that this area should be under the control of Fujian. Try to contact the Fujian Provincial People's Government to see if they have the expertise to manage the Diaoyu Islands, and then apply to them to move your account to the Diaoyu Islands. Second, if you want to live on the island, I suggest you take the whole boat first, or rent one and sit near Diaoyu Island. In order to reduce the target and avoid being discovered by the Japanese, I suggest you swim or dive on the island, and then find a place to settle down on the island. It's just an uninhabited island. It is said that there is fresh water. You may need to learn some fishing skills or hunting skills to ensure that you can survive there. A person's goal is very small, and the chances of finding it for the Japanese are very small. I wish you success! If the Japanese find out, it doesn't matter. Send them back if you can't fight, and your chance to be a hero of the Chinese nation will come true. If you don't find out, you will at least be an unknown Robinson-style legendary hero. I sincerely wish you success.