Jucky,
Simple answer to your dilema
Register your plane in the name of a Ltd Co in which you own all the shares.
The co's registered office address could be for example an Accountants Office, that is what would appear on g-info.
You can hide your shareholding and directorship with nominees.
Your company can opperate at break even, so abreviated returns wont cost much.
Will cost but if your anonimity is so important isnt it worth it?
Put it on N reg and it goes into a trust as a matter of course.
Dont you think you should have kept quiet there are probably a hundred nosey bu**ers out there now deperate to asuage their curiosity and find out who you are