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Wyoming LLC to change it to anonymous

You have to use that company or use some sort of nominee services for a new US LLC with all the headaches that could come with that. Also getting a new password for example from a CBI program could help in your case.
If you focus on having the right nominees and are able to control them so much that they can't do anything without your knowledge, then it can be quite simple. Of course, you need to be very organized for this to be possible.